MA1210 U5 PPT1

Section 2.3
Linear Functions and Slopes

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Section 2.3 Linear Functions and Slopes

The Slope of a Line

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Section 2.3 Linear Functions and Slopes

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

change in y 5  1 6
6
m

 or  change in x 2  3 5
5

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Section 2.3 Linear Functions and Slopes

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Section 2.3 Linear Functions and Slopes

Example

Find the slope of the line passing through the pair of points (5,-2) and (-1,7).

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Section 2.3 Linear Functions and Slopes

First: Plot both points on the graph

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Section 2.3 Linear Functions and Slopes

Next: Draw a line through the points

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Section 2.3 Linear Functions and Slopes

change in y 2  7 9
3
m

 or  change in x 5  (1) 6
2

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Section 2.3 Linear Functions and Slopes

The Point-Slope Form of the Equation of a Line

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Section 2.3 Linear Functions and Slopes

Write the point-slope form of the equation of the line with slope of 3 that passes through (-1,2).
Substitute into the point-slope form; y-y1  m( x  x1 ) y  2  3( x  1) y  2  3( x  1)

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Section 2.3 Linear Functions and Slopes

Solving in Both Forms
A. Write the equation in point slope form of the line with slope 4 that passes through the point (4,-3).
B. Then solve the equation for y. x1 y1

y-y1 = m(x-x1) y-(-3) = 4(x-4)

y+3 = 4(x-4)
-3

-3

y= 4(x-4)-3 y= 4x-16-3

(Slope intercept form)
Substituting the values into the equation

This is point-slope form. Apply the distributive property for the parentheses. This will give us the slope intercept form.
(The equation is solved for y.)

Y = 4x-19

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Section 2.3 Linear Functions and Slopes

Example
Write the point-slope form of the equation of the line with a slope of -4 that passes through (2,5).
Then solve for y.

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Section 2.3 Linear Functions and Slopes

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Section 2.3 Linear Functions and Slopes

Write the point-slope form of the equation of the line that passes through (-1,2) and (-4,5). Then solve for y. y2  y1
52
3
First: Find the slope.
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