Linear Functions: Standard Form and

Slope-Intercept Form

ax + by = cwhere a, b, and c are real numbers and a and b are not both zero.

Examples:-3x + 6y = 12

x + y = 42x + y = -8

Standard Form of a Linear Equation

y = mx + bwhere m = slope and b = y-interceptexample:

y = 2x + 4 m = 2

y-int = 4

Slope-Intercept Form of a Linear Function

You can find the y-intercept by writing the linear equation from standard form to an equivalent equation in slope-intercept form.

A linear equation in standard or slope-intercept form is a linear function.

a. x + y = 4 - x -x

y = -x + 4 m = -1 (slope) y-int = 4

Changing from Standard to Slope-Intercept

a. 2x + y = - 8

- 2x -2x y = -2x - 8 m = -2 (slope) y-int = -8

Changing from Standard to Slope-Intercept

a. -3x + 6y = 12

+ 3x +3x 6y = 3x + 12 6 6 6 -divide each term by 6 y = ½ x + 2 m = ½ (slope) y-int = 2

Changing from Standard to Slope-Intercept

Write the equation in slope-intercept form. Then find the slope and y-intercept.

1. 5x + y = -2 3. 3y - x = -10 2. - 2y = -3 4. 3y = 3.3

You try!

x3

12

You can graph a linear equation using its slope and y-intercept.

Graph 4x + 2y = 8 using the slope and the y-intercept.● Write the equation in the form y = mx + b

4x + 2y = 8 -4x -4x 2y = -4x + 8 2 2 2 y = -2x + 4

m = -2y-int = 4Graph the y-intercept, 4, which is (0,4).

Use the slope, -2, or , to locate another point. Start at (0,4), move 2 units down, and then 1 unit right to arrive at (1,2). From there go down 2 units and then 1 unit to the right to arrive at (2, 0). Draw a line through the three points with arrows at each end.

-2 1

Given the slope and y-intercept of a line, you can write the equation of the line in either slope-intercept form or standard form.

Ex: Write an equation of the line given that its slope is 3 and its y-intercept is -10.

Writing an Equation

m = 3 and y-int = -10

Slope-Intercept Form: y = mx + b y = 3x - 10

Standard Form: ax + by = c y = 3x - 10 -3x + y = -10

Write the equation of a line in slope-intercept form and standard form, given that its slope is 2.5 and y-intercept is -1.

Slope - Intercept Form:

Standard Form:

You Try!

y = 2.5x - 1

-2.5x + y = -1

Given the graph of a line, you can also write the equation of the line.

To write the equation of the line:1. identify the y-intercept.2. Use the coordinates and another point on the line on

the graph to find the slope.3. Write the equation using the slope and y-intercept.

Writing an Equation

The line intersect at the y-axis:(0, -24)y-intercept: -24Use (0, -24) and (-10, -10) to find slope.m = y2 - y1 = -24 - (-10) x2 - x1 0 - (-10) = -14 = -7 = -1 ⅖ = m 10 5So, the equation is y = -1⅖x - 24

Find the slope and y-intercept of each line. Then write the equation.

y-intercept: -2slope: -1

equation: y = -x - 2

You try!