College Alg/Trig
2.3 Linear Functions & Slope
Name: ___________________________
The ______________________ of a line is a useful measure of the steepness of a line.
Slope compares the vertical change known as ____________________ to the horizontal change
known as the run.
Definition of Slope: Given two distinct points (𝑥1 , 𝑦1 ) and (𝑥2 , 𝑦2 ) the slope is…
Examples: Find the slope of the line passing through each pair of points.
1. (−3, −1) 𝑎𝑛𝑑 (−2, 4)
2. (−3, 4) 𝑎𝑛𝑑 (2, −2)
3. (4, −2) 𝑎𝑛𝑑 (−1, 5)
What happens to the slope if we get a zero in either the numerator or the denominator?
Numerator
Denominator
Ex. (−2, 5) and (1, 5)
Ex. (5, −1) and (5, 3)
Positive
Types of Slopes and What They Look Like:
Negative
Zero
Undefined
Writing Equations of Lines
1. Point-Slope Form
2. Slope Intercept Form
3. Horizontal Line
4. Vertical Line
5. General Form
Most generally we see lines in ______________________________. This helps us when it comes to
graphing.
Using Slope-Intercept Form:
Write the equation of a line given the following information. Then identify the type of slope and
whether the line is rising, falling, horizontal or vertical.
1. A line with a slope of 4 and 2. A line with a slope of -2 and 3. A line with a slope of − 2
3
a y-intercept of –1.
a y-intercept of 3.
and a y-intercept of 0.
Horizontal and Vertical Lines:
Horizontal and Vertical Lines are special cases of lines due to the nature of their slopes.
Horizontal lines have a _________________ slope.
You will know you have a horizontal line, when the y-coordinates of each point are the same.
Vertical lines have an _______________________ slope.
You will know you have a vertical line when the x-coordinates of each point are the same.
Using Point-Slope Form to write the equation of a line.
Type 1: Given a point and the slope.
Ex 1. Write the point-slope form of a line with
Ex 2. Write the equation in point-slope for the
a slope of 4 that passes through the point
line with a slope of -2 that passes through the
(-1, 3). Then solve the equation for y.
point (2, -4). Then solve the equation for y.
Type 2: Given two points.
First you will have to find the _______________________ between the two points.
Then you can plug into the equation, and rearrange the equation for y.
Ex 1. Write an equation in point-slope form for
the line passing through the points
(−2, −1) 𝑎𝑛𝑑 (−1, −6).
Ex 2. Write an equation in point-slope form for
the line passing through the points
(4, −3) 𝑎𝑛𝑑 (−2, 6).
Step 1: Find the slope.
Step 1: Find the slope.
Step 2: Plug into the equation.
Step 2: Plug into the equation.
Now you try… Write the equation of a line in (1) point-slope form and (2) slope-intercept form
given the following…
1. Slope = −5, passing through (1, −7).
2. Passing through (−4, 2) and (1, 5).
1
3. 𝑥 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 = − 2 , 𝑎𝑛𝑑 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 = 4.
4. 𝑃𝑎𝑠𝑠𝑖𝑛𝑔 𝑡ℎ𝑟𝑜𝑢𝑔ℎ (2, −5) 𝑎𝑛𝑑 (2, 8)