UNIT 2 LESSON 2

SLOPE & EQUATIONS OF LINES

COLLEGE PREP

WARM UP

OBJECTIVES

•Find the slope of a line from a graph

•Find the slope of a line given 2 points

•Graph a line that is in slope-intercept form (𝑦 = 𝑚𝑥 + 𝑏)

•Write the equation of a line in slope-intercept form given

a graph or a set of two points

•Use the point-slope form of the equation to write the

equation of a line

SLOPE-INTERCEPT FORM

Standard Form: A𝑥 + B𝑦 = C

If the standard form of a line is solved for 𝑦, a new form is created: slope-intercept form:

𝑦 = 𝑚𝑥 + 𝑏where 𝑚 is the slope and 𝑏 is the 𝑦-intercept.

SLOPE-INTERCEPT FORM

Write the equation in slope-intercept form.

Identify the slope and the 𝑦-intercept.

A) 3𝑥 + 4𝑦 = 20

SLOPE-INTERCEPT FORM

Write the equation in slope-intercept form.

Identify the slope and the 𝑦-intercept.

B) 5𝑥 − 𝑦 = 7

SLOPE

Slope is the ratio of the change in 𝑦 to the change in 𝑥.

𝑅𝐼𝑆𝐸 (𝑦)

𝑅𝑈𝑁 (𝑥)=change in 𝑦

change in 𝑥=𝑦2 − 𝑦1𝑥2 − 𝑥1

SLOPE

Use the given point and slope to find a second point on

the graph.

C) Point: (1, −3) D) Point: (−2,10)

Slope: 3

4Slope: −3

SLOPE-INTERCEPT FORM

E) Graph 𝑦 = −2

3𝑥 + 2

SLOPE-INTERCEPT FORM

F) Graph 𝑦 = 5𝑥 − 1

SLOPE-INTERCEPT FORM

G) Graph 3𝑥 + 2𝑦 = −4

SLOPE-INTERCEPT FORM

H) A 𝑦-intercept of 3 is shown at (0,3).Use this intercept to create the following:

Draw a line with a positive slope.Find the equation of that line.

Draw a line with a negative slope.Find the equation of that line.

SLOPE-INTERCEPT FORM

I) Write the equation of the line shown.

SLOPE-INTERCEPT FORM

Find the slope of the following graphs:

J) K)

SLOPE-INTERCEPT FORM

Find the slope of the line that passes through the points:

L) 3,4 , (6, −8) M) 1,2 , (−3,−7)

POINT-SLOPE FORM

Point-Slope form uses a point and the slope to create a

linear equation. Using a point (𝑥1, 𝑦1) and a slope 𝑚

𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1)

POINT-SLOPE FORM

𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1)

N) What is the equation of the line that has a slope of 3

and goes through (3,5)?

POINT-SLOPE FORM

𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1)

O) What is the equation of the line that has a slope of −2and goes through (−1,2)?

POINT-SLOPE FORM

P) What is the equation of the line that goes through

−2,3 and (1, −1)?

HINT: What do today’s two formulas for a line have in

common?

POINT-SLOPE FORM

Q) Find a linear function 𝑓 such that 𝑓 2 = 7 and

𝑓 3 = 4. What is 𝑓(5).

OBJECTIVES

•Find the slope of a line from a graph

•Find the slope of a line given 2 points

•Graph a line that is in slope-intercept form (𝑦 = 𝑚𝑥 + 𝑏)

•Write the equation of a line in slope-intercept form given

a graph or a set of two points

•Use the point-slope form of the equation to write the

equation of a line

HOMEWORK

In Class Assignment 2.2

Homework 2.2

EDPuzzle 2.2