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May 24th

May 24th

# UNDERSTANDING GRAPHS OF LINEAR EQUATIONS

Recall that the slope- intercept form of a linear equation is y = mx + b where m is the
slope and b is the y - coordinate of the y -intercept

Recall that the point-slope of a linear equation is where m is the slope
and   is a given point on the line

Don’t forget that the slope measures the change in the y -coordinate relative to the
change in the x-coordinate, or, more precisely,

Model Problems:

1. What are the slope and the y-intercept of the fol lowing linear equation?

 6x + 2 = 2y − 7 y = 3x + 4.5 Solve the original equation for y and read off m and b

Answer: m = 3 and y-int = (0,4.5)

2. Find the slope of the line which passes through the points (5,100) and (8,67).

3. Find the equation of the line which passes through the points (5,100) and (8,67).
Using the above result, we know that m = −11

 y −100 = −11(x − 5) Here we’re using the point-slope form y −100 = −11x + 55 Distribute −11 y = −11x +155 Solve for y

4. Find an equation of the line graphed on the right :

 m = −2 Choose any two clear points, like (2, 0) and (0, 4), and use the slope formula y-int = (0, 4) Simply read off the graph Answer: y = −2x + 4

Practice Exercises:

1. Which of the following equations is most likely re presented by the given graph?

2. Which of the following graphs most likely represents the equation y = −2.1x + 50?

3. Which of the following graphs most likely represents the equation y = 3.11x −10?

Given a pair of points below, find the slope of the line which passes through them.

4. (5, 2) and (-1, 1)

5. (12, -4) and (10, 10)

6. (1, 4) and (-10, 4)

Find the equation of the line which passes through the given points.

7. (3, -5) and (8, 5)

8. (10, 3) and (15, -17)

9. (1.2, 4) and (2.2, 5)

Find the slope and the y-intercept of the lines whose equations are given below.

10. 2y − 2 = 6x

11. 10y + 3 = −20x − 20

12. 110x +1 = 100y −1

1. (c)

2. (a)

3. (b)

4.

5. − 7

6. 0

7. y = 2x −11

8. y = −4x + 43

9. y = x + 2.8

10. slope = 3, y int = (0,1)

11. slope = −2, y int = (0,−2.3)

12. slope = 1.1, y int = (0,0.02)

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