5.1 write linear equations in slope-intercept .write linear equations in slope-intercept form goal

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  • Copyright Holt McDougal. All rights reserved. Lesson 5.1 Algebra 1 Notetaking Guide 119

    Write Linear Equations inSlope-Intercept FormGoal p Write equations of lines.

    5.1

    Your Notes

    Write an equation of the line with a slope of 24 and a y-intercept of 6.

    Solutiony 5 mx 1 b Write slope-intercept form.

    y 5 x 1 Substitute for m and for b.

    Example 1 Use slope and y-intercept to write an equation

    Checkpoint Write an equation of the line with the given slope and y-intercept.

    1. Slope is 8; 2. Slope is 2 } 3 ;

    y-intercept is 25. y-intercept is 22.

    3. Slope is 23; 4. Slope is 2 5 } 2 ;

    y-intercept is 7. y-intercept is 9.

    Use the slope-intercept form (y 5 mx 1 b) to write an equation of a line if slope and y-intercept are given.

  • Copyright Holt McDougal. All rights reserved. Lesson 5.1 Algebra 1 Notetaking Guide 119

    Write Linear Equations inSlope-Intercept FormGoal p Write equations of lines.

    5.1

    Your Notes

    Write an equation of the line with a slope of 24 and a y-intercept of 6.

    Solutiony 5 mx 1 b Write slope-intercept form.

    y 5 24 x 1 6 Substitute 24 for m and 6 for b.

    Example 1 Use slope and y-intercept to write an equation

    Checkpoint Write an equation of the line with the given slope and y-intercept.

    1. Slope is 8; 2. Slope is 2 } 3 ;

    y-intercept is 25. y-intercept is 22.

    y 5 8x 1 (25) y 5 2 } 3 x 1 (22)

    3. Slope is 23; 4. Slope is 2 5 } 2 ;

    y-intercept is 7. y-intercept is 9.

    y 5 23x 1 7 y 5 2 5 } 2 x 1 9

    Use the slope-intercept form (y 5 mx 1 b) to write an equation of a line if slope and y-intercept are given.

  • Your Notes

    120 Lesson 5.1 Algebra 1 Notetaking Guide Copyright Holt McDougal. All rights reserved.

    Write an equation of the line shown.

    SolutionStep 1 Calculate the slope.

    x

    y

    1

    3

    12121

    23

    23 3

    (3, 22)

    (0, 4)

    m 5 y2 2 y1 } x2 2 x1

    5 2

    2

    5 5

    Step 2 Write an equation of the line. The line crosses the y-axis at . So, the y-intercept is .

    y 5 mx 1 b Write slope-intercept form.

    y 5 x 1 Substitute for m and for b.

    Example 2 Write an equation of a line given two points

    You can write an equation of a line if you know the y-intercept and any other point on the line.

    5. Write an equation of the line shown.

    x

    y1

    12121

    23

    25

    3 5

    (5, 23)

    (0, 26)

    Checkpoint Complete the following exercise.

  • Your Notes

    120 Lesson 5.1 Algebra 1 Notetaking Guide Copyright Holt McDougal. All rights reserved.

    Write an equation of the line shown.

    SolutionStep 1 Calculate the slope.

    x

    y

    1

    3

    12121

    23

    23 3

    (3, 22)

    (0, 4)

    m 5 y2 2 y1 } x2 2 x1

    5 3

    22

    0

    4

    2

    2

    5 3

    26 5 22

    Step 2 Write an equation of the line. The line crosses the y-axis at (0, 4) . So, the y-intercept is 4 .

    y 5 mx 1 b Write slope-intercept form.

    y 5 22 x 1 4 Substitute 22 for m and 4 for b.

    Example 2 Write an equation of a line given two points

    You can write an equation of a line if you know the y-intercept and any other point on the line.

    5. Write an equation of the line shown.

    y 5 3 } 5 x 2 6

    x

    y1

    12121

    23

    25

    3 5

    (5, 23)

    (0, 26)

    Checkpoint Complete the following exercise.

  • Your Notes

    Write an equation for the linear function f with the values f(0) 5 4 and f(2) 5 12.

    Solution

    Step 1 Write f(0) 5 4 as and f(2) 5 12 as .

    Step 2 Calculate the slope of the line that passes through and .

    m 5 y2 2 y1 } x2 2 x1

    5 2

    2

    5

    5

    Step 3 Write an equation of the line. The line crosses the y-axis at (0, ). So, the y-intercept is .

    y 5 mx 1 b Write slope-intercept form.

    y 5 Substitute for m and for b.

    The function is .

    Example 3 Write a linear function

    Homework

    6. Write an equation for the linear function with the values f(0) 5 3 and f(3) 5 15.

    Checkpoint Complete the following exercise.

    Copyright Holt McDougal. All rights reserved. Lesson 5.1 Algebra 1 Notetaking Guide 121

  • Your Notes

    Write an equation for the linear function f with the values f(0) 5 4 and f(2) 5 12.

    Solution

    Step 1 Write f(0) 5 4 as (0, 4) and f(2) 5 12 as (2, 12).

    Step 2 Calculate the slope of the line that passes through (0, 4) and (2, 12).

    m 5 y2 2 y1 } x2 2 x1

    5 2

    12

    0

    4

    2

    2

    5 2

    8

    5 4

    Step 3 Write an equation of the line. The line crosses the y-axis at (0, 4 ). So, the y-intercept is 4 .

    y 5 mx 1 b Write slope-intercept form.

    y 5 4x 1 4 Substitute 4 for m and 4 for b.

    The function is f (x) 5 4x 1 4.

    Example 3 Write a linear function

    Homework

    6. Write an equation for the linear function with the values f(0) 5 3 and f(3) 5 15.

    y 5 4x 1 3

    Checkpoint Complete the following exercise.

    Copyright Holt McDougal. All rights reserved. Lesson 5.1 Algebra 1 Notetaking Guide 121

  • 5.2 Use Linear Equations inSlope-Intercept FormGoal p Write an equation of a line using points

    on the line.

    WRITING AN EQUATION OF A LINE IN SLOPE-INTERCEPT FORM

    Step 1 Identify the slope . You can use the to calculate the slope if you know

    two points on the line.

    Step 2 Find the . You can substitute the and the of a point (x, y) on the line into y 5 mx 1 b. Then solve for .

    Step 3 Write an equation using .

    Your Notes

    Write an equation of the line that passes through the point (1, 2) and has a slope of 3.

    Solution

    Step 1 Identify the slope. The slope is .

    Step 2 Find the y-intercept. Substitute the slope and the coordinates of the given point into y 5 mx 1 b. Solve for b.

    y 5 mx 1 b Write slope-intercept form.

    5 ( ) 1 b Substitute for m, for x, and for y.

    5 b Solve for .

    Step 3 Write an equation of the line.

    y 5 mx 1 b Write slope-intercept form.

    y 5 Substitute for m and for b.

    Example 1 Write an equation given the slope and a point

    Be careful not to mix up the x- and y-values when you substitute.

    Your NotesYour Notes

    122 Lesson 5.2 Algebra 1 Notetaking Guide Copyright Holt McDougal. All rights reserved.

  • 5.2 Use Linear Equations inSlope-Intercept FormGoal p Write an equation of a line using points

    on the line.

    WRITING AN EQUATION OF A LINE IN SLOPE-INTERCEPT FORM

    Step 1 Identify the slope m . You can use the slope formula to calculate the slope if you know two points on the line.

    Step 2 Find the y-intercept . You can substitute the slope and the coordinates of a point (x, y) on the line into y 5 mx 1 b. Then solve for b .

    Step 3 Write an equation using y 5 mx 1 b .

    Your Notes

    Write an equation of the line that passes through the point (1, 2) and has a slope of 3.

    Solution

    Step 1 Identify the slope. The slope is 3 .

    Step 2 Find the y-intercept. Substitute the slope and the coordinates of the given point into y 5 mx 1 b. Solve for b.

    y 5 mx 1 b Write slope-intercept form.

    2 5 3 ( 1 ) 1 b Substitute 3 for m, 1 for x, and 2 for y.

    21 5 b Solve for b .

    Step 3 Write an equation of the line.

    y 5 mx 1 b Write slope-intercept form.

    y 5 3x 2 1 Substitute 3 for m and 21 for b.

    Example 1 Write an equation given the slope and a point

    Be careful not to mix up the x- and y-values when you substitute.

    Your NotesYour Notes

    122 Lesson 5.2 Algebra 1 Notetaking Guide Copyright Holt McDougal. All rights reserved.

  • Your Notes

    1. Write an equation of the line that passes through the point (2, 2) and has a slope of 4.

    Checkpoint Complete the following exercise.

    Write an equation of the line that passes through (2, 23) and (22, 1).

    SolutionStep 1 Calculate the slope.

    m 5 y2 2 y1 } x2 2 x1

    5 2

    2

    5 5

    Step 2 Find the y-intercept. Use the slope and the point (2, 23).

    y 5 mx 1 b Write slope-intercept form.

    23 5 ( ) 1 b Substitute for m, for x, and

    for y.

    5 b Solve for b.

    Step 3 Write an equation of the line.

    y 5 mx 1 b Write slope-intercept form.

    y 5 Substitute for m and for b.

    Example 2 Write an equation given two points

    You can also find the y-intercept using the coordinates of the other given point.

    Copyright Holt McDougal. All rights reserved. Lesson 5.2 Algebra 1 Notetaking Guide 123

  • Your Notes

    1. Write an equation of the line that passes through the point (2, 2) and has a slope of 4.

    y 5 4x 2 6

    Checkpoint Complete the following exercise.

    Write an equation of the line that passes through (2, 23) and (22, 1).

    SolutionStep 1 Calculate the slope.

    m 5 y2 2 y1 } x2 2 x1

    5 22

    1

    2

    (23)

    2

    2

    5 24

    4 5 21

    Step 2 Find the y-intercept. Use the slope and the point (2, 23).

    y 5 mx 1 b Write slope-intercept form.

    23 5 21 ( 2 ) 1 b Substitute 21 for m, 2 for x, and 23 for y.

    21 5 b Solve for b.

    Step 3 Write an equation of the line.

    y 5 mx 1 b Write slope-intercept form.

    y 5 2x 2 1 Substitute 21 for m and 21 for b.

    Example 2 Write an equation given two points

    You c

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