# MCC85 & MCC86. Students will graph and analyze graphs of linear equations. a. Interpret slope as a rate of change. b. Determine the meaning of the slope.

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MCC85 & MCC86. Students will graph and analyze graphs of linear equations. a. Interpret slope as a rate of change. b. Determine the meaning of the slope and y-intercept in a given situation.

Slope is a measure of Steepness.

Types of Slope Zero Negative Positive Undefined or No Slope

Slope can be expressed different ways:
A line has a positive slope if it is going uphill from left to right. A line has a negative slope if it is going downhill from left to right. 4

What are the steps to determine the slope given two points?
Label your two points (X1,Y1) and (X2, Y2) Write the formula Y2- Y1 X2- X1 3. Substitute 4. Solve

3) Find the slope of the line that goes through the points (-5, 3) and (2, 1).

Find the slope of the line through the points (3,7) and (5, 19). x1 y1
m = 19 – 7 5 – 3 m = 12 2 m = 6

Determine the slope given two points.
1. (-9,0) (5,7) 2. (-4,-3) (0,-3) 3. (6,6) (-5,-2) 4. (7,2) (-8,2) 5. (4,-1) (1,1) 6. (0,0) (-5,-6) 7. (-7,-8) (2,2) 8. (-6,4) (7,0) 9. (13,12) (-10,15) 10. (9,2) (20, -5)

Determining Slope using a graph

On the piece of graph paper
Choose any two points on the line. Write down the two points. Label the two points with (X1, Y1) (X2, Y2) Write the formula Substitute Solve

Is there an easier way??? YES!!!
Slope is how your line changes up/over! Soooooo…. Pick any two points Count the number of spaces you move up. Count the number of spaces you move over. This is your slope! If you move up and to the right, your slope is positive. If you move up and to the left, your slope is negative!

Determine the slope of the line.
Start with the lower point and count how much you rise and run to get to the other point! rise 3 = = run 6 6 3 Notice the slope is positive AND the line increases! 12

What is the slope of a vertical line?
The line doesn’t run! All vertical lines have an undefined slope.

What is the slope of a horizontal line?
The line doesn’t rise! All horizontal lines have a slope of 0.

Don’t worry! Pick any two points that are on the line! Your answer will be the same (when you put it in lowest terms) no matter which two points you pick!

If given an equation of a line, there are 2 ways to find the slope and y-intercept.

One method is to write the equation in slope-intercept form,
which is y = mx + b. slope y-intercept

y = 3x + ½ Find the slope and y-intercept of the following equations.

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