Recall Graphing from Slope-Intercept Form

2.3 Graphs of Linear EquationsName:

●Recall – graphing from Slope-Intercept Form

Example 1: f(x) = x ‒ 3Example 2:y = ‒3x + 4

m: slope: m: slope:

b: y-intercept: b: y-intercept:

●Finding slope from two points

Example 3: a. Find the slope using the formula given (‒3, 4) and (5, ‒8)

x1 y1 x2 y2

Substitute into the formula m = = =

b. (2, 1) and (0, 0)c. (8, ‒4) and (‒6, ‒3)

d. e.

f. Do the points (1, 5), (2.5, 9.5) and (4.5, 15.5) lie on the same line? Prove your answer.

● Are all lines functions? Equations of Horizontal and Vertical Lines

Use the graph below right to complete the table.

a. What type of line is this?

b. Use the definition of a function to determine from the table if this is a function.

c. Use the vertical line test to determine if the

graph is a function.

d. Find the y-intercept and the slope then write

the equation of the line.

slope (m):y-intercept (b):

equation:

e. On the same coordinate plane graph y = 4 and y = ‒1. What is the slope of allhorizontal lines?

Use the graph below right to complete the table.

a. What type of line is this?

b. Use the definition of a function to determine from the table if this is a function.

c. Use the vertical line test to determine if the

graph is a function.

d. Find the slope of the line using the formula.

e. On the same coordinate plane graph x = 2 and x = ‒4. What is the slope of allvertical lines?

● Slope and Steepness of a Line

a. Which line from the graph is the steepest?

b. Which is the least steep?

c. Use the slope triangles to find the slope of each line.

Line A: ______Line B: ______

Line C: ______Line D: ______

d. Find the absolute value of each slope then write

in order from least steep (flattest) to steepest.

e. Compare the steepest line to the least steep (flattest) line.

Which is increasing or decreasing at the fastest rate?

Practice:

Graph each linear equation.

1. f(x) = x ‒ 3 2. y = ‒3x + 43. x = ‒1

m: slope: m: slope: m: slope:

b: y-intercept: b: y-intercept: b: y-intercept:

4. y = ‒x + 2 5. y = 36.f(x) = ‒x + 3

m: slope: m: slope: m: slope:

b: y-intercept: b: y-intercept: b: y-intercept:

Use the slope formula to find the slope of each line.

7. (1, 0) and (‒4, 2) 8.(‒2, 3) and (6, 5) 9. (3, 8) and (7, 3)

10. 11.

12. Do the points (2, 5), (4, 3.5), and (7, 1.5) lie on the same line? Prove your answer.

Use the graph at the right to answer the following.

13. Which line from the graph is the steepest?

14. Which is the least steep?

15. Use the slope triangles to find the slope of each line.

Line A: ______Line B: ______

Line C: ______Line D: ______

Line E: ______

16. Find the absolute value of each slope then write in order from least steep (flattest) to steepest.

17. Compare the steepest line to the least steep (flattest) line. Which is increasing or decreasing at the

fastest rate?

18. Graph a line to match each description below.

Label each line.

A y = x ‒ 1

B A line with Δx= 4 and Δy= −6

passing through the origin.

C f(x) = x–7

D x = –6

F A horizontal line with a y-intercept of (0, ‒2)