1. 3.3 & 3.4 Slope & Finding the equation of a Line
Learning Goals
Find the slope of a line and graph a line given its slope and a point on it
Find the equation of a line given its slope and a point on the line, or two points, or its slope and the y-intercept

2. slope
steepness of a line
the ratio of the vertical change to the horizontal change
“rise over run”
*special cases: HOY VUX
slope-intercept form:
𝑚= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1
𝑦=𝑚𝑥+𝑏

3. Ex 2
Ex 1
𝑦=− 4 3 𝑥+2
Graph
Find the slope.
−2,7 and 8,−6

4. Ex 3
Graph
𝑥+2𝑦=−2

5. Ex 4
Ex 5
Write an equation in slope-intercept form of the line that passes through
Find the slope of the line.
−7𝑥+2𝑦=8
4,−3 and 5,−1

6. Formulas and Key info to KNOW
slope:
slope of parallel lines:
point-slope form:
*HOY
slope-intercept form:
slope of perpendicular lines:
standard form:
*VUX
𝑚= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1
𝑦=𝑚𝑥+𝑏
𝑠𝑎𝑚𝑒 𝑠𝑙𝑜𝑝𝑒
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑟𝑒𝑐𝑖𝑝𝑟𝑜𝑐𝑎𝑙 𝑠𝑙𝑜𝑝𝑒𝑠
𝑦− 𝑦 1 =𝑚 𝑥− 𝑥 1
𝐴𝑥+𝐵𝑦=𝐶

7. Ex 6
Ex 7
Write an equation in point-slope form of the line with a slope of 3 and passing through
Write an equation in standard form of the line
𝑦= 3 4 𝑥−5
−1,5

8. Ex 8
Ex 9
Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the given line.
If the slope of a line is 3, find the slopes of lines parallel and perpendicular to the line.
5,−3
𝑦=4𝑥+1

9. Ex 10
Ex 11
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the x-axis.
Write an equation in slope-intercept and standard forms of the line with a slope of − and passing through
8,−1
−2,5

10. Writing Equations of Lines Summary
slope-intercept form
point-slope form
standard form
𝑦=𝑚𝑥+𝑏
𝑦− 𝑦 1 =𝑚 𝑥− 𝑥 1
𝐴𝑥+𝐵𝑦=𝐶
Handy for graphing and comparing slopes
Use when given:
slope & y-intercept
point & slope
two points
Provides an easy way to find both intercepts and graph