Graphing &
Slope
Learn how to graph lines and understand slope with confidence.
What You’ll Learn:
-
Graph a line from slope-intercept form -
Calculate the slope between two points
-
Write a line in slope-intercept form -
Interpret a line’s slope and graph
Lesson 1:
Slope-Intercept Form
Identify the slope and y-intercept .
Example:
y = mx + b
y = 2x + 1
m = 2
slope
b = 1
y-intercept
Lesson 2:
Finding the Slope Between Two Points
Use the Slope formula.
Example:
Given points
(1, 2)
and
(6, 10),
find the slope:
m =
y₂ − y₁
x₂ − x₁
m =
10 − 2
6 − 1
m =
8
5
slope =
8
5
Practice Problems
Easy
y = −2x + 3
Graph a line
Medium
(2, 4) and (6, 10)
Find the slope
Challenge
Write the equation of the line
through (3, -5) with slope -3/5
Solutions
Easy
Graph y= -2x+3
Y-intercept is (0, 3). Slope is -2, so from there go down 2, right 1. Plot a second point at (1, 1) and draw
the line.
Medium
Find the slope through (2, 4) and (6, 10)
slope = (10-4)/(6-2) = 6/4 = 3/2
Challenge
Equation of line through (3, -5) with slope -3/5
Use point-slope form: y -(-5)=-3/5(x-3)
y + 5 = -3/5(x-3)
y=-3/5x+9/5-5
y=-3/5x+9/5-25/5
y = -3/5x-16/5
Common Mistakes to Avoid:
-
Mixing up the rise and run -
Incorrect sign for the slope -
Plotting the y-intercept incorrectly
Quick Recap:
Slope-Intercept Form y = mx + b
Point-Slope Form y-y₁ = m(x-x₁)
Point-Slope Form y-y₁ = m(x-x₁)
Point-Slope Form y-y₁ = m(x-x₁)
(a point on the line)
Standard Form Ax + By = C
Answer Key:
Easy:
Graph y= -2x+3
Y-intercept is (0, 3). Slope is -2, so from there go down 2, right 1. Plot a second point at (1, 1) and draw the line.
Medium:
Find the slope through (2, 4) and (6, 10)
slope = (10-4)/(6-2) = 6/4 = 3/2
Challenge:
Equation of line through (3, -5) with slope -3/5
Use point-slope form: y -(-5)=-3/5(x-3)
y + 5 = -3/5(x-3)
y=-3/5x+9/5-5
y=-3/5x+9/5-25/5
y = -3/5x-16/5
Next:
Systems of Equations
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