Chapter 4

Algebra I and Concepts

Day 1, Section 4-1: Graphing in Slope-Intercept Form

Slope-Intercept Form: Any equation written in the form y = mx + bm: b:

Which of the following are in slope intercept form? Are any in standard form?a) 4y = 2x + 6 b) y = 3x – 5c) 2x – 5y = 12

Day 1, Section 4-1: Graphing in Slope-Intercept Form

Ex) Identify the slope and the y-intercept of the following equationsa) y = ½x – 5 b) y = x + 7 c) 2x – 3y = 12

Ex) Write an equation of a line in slope-intercept form, given the slope and the y-intercepta) Slope: 4, y-intercept: -2 a) m = 6, b = 12

Day 1, Section 4-1: Graphing in Slope-Intercept Form

Steps to Graphing an equation in slope-intercept form. Ex) 1) Plot the ________________2) Count the slope________ over _________, And plot a second point3) Draw a line connecting The 2 points

Day 1, Section 4-1: Graphing in Slope-Intercept Form

Slope MovementPositive Numbers: UP/RIGHT

Negative Number: DOWN/LEFT

Ex) Graph the following equations using slope-intercept form methoda) b) y = 5x + 8

c) 5x – 3y = 15

Day 2: Section 4-1, Horizontal and Vertical Lines

Graphing Horizontal LinesEquations look like this: y = a number (there is NO x variable!)To Graph:1) Draw a horizontal line through that numberGraph y = -2

Graphing Vertical LinesEquations look like this:

x = a number(there is NO y variable)To Graph:1) Draw a vertical line through that numberGraph x = 6

Day 2: Section 4-1, Horizontal and Vertical Lines

Graph the following lines. First determine if the line is horizontal, vertical, or oblique.1) y = 4 2) y = -2x + 4

3) x = -1

Day 2: Section 4-1

Write an equation in slope-intercept form for the graph pictured1) 2)

3)

Day 1, Section 4-2: Writing Equations in Slope-Intercept Form

Writing equations in slope-intercept form when given the slope and a point.Steps(USE y = mx + b) Example: slope = 2, (-3, 5)1) Plug the slope in for m2) Plug the point in for

x and y3) Solve for b4) Write the equationUsing the given m and The b you just found

Day 1, Section 4-2: Writing Equations in Slope-Intercept Form

Write a equation for the line using the information given. Use slope-intercept form1) (3, 1), slope 2 2) (-1, 4),

slope -1

Day 2: Section 4-2, Writing Equations in Slope Intercept Form

Write an equation in slope intercept form of a line through the 2 points: (3, 1) and (2, 4)Steps (use y = mx + b)Example: 1) Use the 2 points and theSlope formula to find m2) Use m and one point andPlug into y = mx + b to find b3) Re-write the equation

Day 2: Section 4-2, Writing Equations in Slope Intercept Form

Write an equation in slope intercept form of a line through the 2 points: a) (-4, -2) and (-5, -6) b) (-1, 12) and (4, -8)

Day 1: Section 4-3, Point-Slope Form

Point-Slope Form: given a point , and the slope, an equation can be written such that

Name Equation When to use it

Slope-Intercept Form

Point-Slope From

Standard Form Only when converting from a previous form

Day 1: Section 4-3, Point-Slope Form

Ex) Write an equation in point-slope form for a line that passes through the point (3, -2) and has a slope of ¼ . Then graph the line.

Day 1: Section 4-3, Point-Slope Form

Identify the slope and the given point in each of the equations that are in point-slope form.1) y – 3 = 10(x + 4) 2) y + 5 = -2(x +6)

3) y + 1 = x – 5 4) y – 8 = -x

Day 1: Section 4-3, Point-Slope Form

Graph the equations that are in point-slope form.1) y – 2 = 3(x + 4) 2) y + 8 = -½ (x – 1)

Day 2: Section 4-3, Re-writing equations

Ex) Write in standard form

Ex) Write in slope-intercept form

Day 2: Section 4-3, Write an Equation using a Picture of the Graph

Write an equation for each line in point-slope form and then convert the equation to slope-intercept form AND standard form.

Day 1: Section 4-4, Parallel Lines

Parallel Lines – lines that do not intersect and have the SAME SLOPE!Which of the following lines are parallel? Note: you must be able to identify the slope in each equation!a)b)c)d)e)

Day 1: Section 4-4, Parallel LinesWrite an equation in slope-intercept form for the line that passes through (-3, 5) and is parallel to the line y = 2x – 4Steps

Example1) Find the slope you need(remember about slopes Of parallel lines!)2) Use m and the point toPlug into y = mx +b and Solve for b3) Re-write the equation

Day 1: Section 4-4, Parallel Lines

Ex1) Write an equation in slope-intercept form for a line parallel to y = 3x – 5 and through the point (4, -3)

Ex2) Write an equation in slope-intercept form for a line parallel to y = -½x + 6 and through the point (-4, 2)

Day 2: Section 4-4 Perpendicular Lines

Opposite Reciprocals – 2 numbers whose product is -1. Flip and switch the sign!Perpendicular Lines - Lines that intersect to form a right angle. Perpendicular lines have slopes that are opposite reciprocals.Ex) Find the opposite reciprocals of the following numbersa) 3 b) -5 c) ½

d) -¾

Day 2: Section 4-4 Perpendicular Lines

Write an equation in slope-intercept form for the line that passes through (8, 2) and is perpendicular to the line y = -4x + 5StepsExample1) Find the slope you need(remember about slopes Of perpendicular lines!)2) Use m and the point toPlug into y = mx +b and Solve for b3) Re-write the equation

Day 2: Section 4-4 Perpendicular Lines

Ex1) Write an equation in slope-intercept form for a line perpendicular to y = x + 4 and through the point (3, -2)

Ex2) Write an equation in slope-intercept form for a line perpendicular to and through the point (-2, 3)

Day 2: Section 4-4, Comparing Lines Determine if the lines are parallel, perpendicular, or neither.1)

2)

3)4)

Section 4-5, Scatterplots

Scatterplot – a graph showing the relationship between a set of data with 2 variables

Section 4-5, Scatterplots

Ex) What kind of correlation does the graph have? Describe its meaning.

Section 4-5, Scatterplots

Section 4-5: Scatterplots

Section 4-5: Scatterplots