Virginia SOL Math / Grade 8 / Patterns, Functions & Algebra
Linear Functions & Slope
What you'll learn
- Determine the slope of a line from a graph, table, or equation
- Graph a linear function using slope and y-intercept
- Interpret slope and intercept in context
Words to know
- Slope —
- the steepness of a line, rise over run
- y-intercept —
- where a line crosses the y-axis
- Linear function —
- a function whose graph is a straight line
- Slope-intercept form —
- the equation y = mx + b
- Rate of change —
- how much the output changes per unit of input
Why it matters Linear functions model steady change, like a phone plan or a savings goal, where slope is the rate and the intercept is the start.
Worked examples
Model ItI do
Find the slope through the points (1, 2) and (4, 11).
Slope is the change in y over the change in x. That is (11 - 2) divided by (4 - 1) = 9 divided by 3 = 3. The slope is 3.
Try It TogetherWe do
For y = 2x + 5, name the slope and y-intercept.
The equation is in slope-intercept form y = mx + b. So the slope m is 2 and the y-intercept b is 5, meaning the line crosses the y-axis at (0, 5).
Now YouYou do
Find the slope through the points (2, 3) and (6, 15).
Use the change in y over the change in x. Check your answer in the back of this chapter.
Practice
Mastered 0 of 11
Warm-up
Ease in with the basics.
1.Find the slope through (0, 0) and (3, 6).
2.Name the slope of y = 5x + 2.
3.Name the y-intercept of y = 2x - 9.
On Level
The core Quick Check from the book.
1.Find the slope through (0, 0) and (2, 8).
2.Name the slope of y = -4x + 1.
3.Name the y-intercept of y = 3x - 7.
4.Find the slope through (1, 5) and (3, 5).
5.As x increases by 1, y increases by 6. What is the slope?
Challenge
Stretch your thinking.
1.Find the slope of the line through (-1, 3) and (2, -6).
2.A phone plan costs y = 15x + 20 dollars, where x is gigabytes used. What does the slope 15 and the intercept 20 mean?
3.A line has slope 4 and passes through (0, -3). Write its equation in slope-intercept form.