Chapter 3 Lesson 2 homework practice slope answers come easier when you understand the idea behind the formula instead of just memorizing steps. This guide walks through everything that lesson usually covers — finding slope from a graph, from a table, and from two ordered pairs — with worked examples, answers, common mistakes to avoid, and a quick FAQ so you can check your homework with confidence.
What Slope Actually Means
Slope measures how steep a line is and which direction it moves. In plain language, it answers the question: for every step I take sideways, how far do I go up or down?
That is why slope is also called rate of change. If a line has a slope of 3, then every time x increases by 1, y increases by 3.
The formal definition is:
slope = rise ÷ run, or m = (change in y) ÷ (change in x)
In the equation y = mx + b, the letter m stands for slope, and b is the y-intercept. Keeping those two letters straight matters, because homework problems often ask you to identify one or the other Practical, not theoretical..
The Slope Formula You Will Use Most
When you are given two points, use:
m = (y₂ − y₁) / (x₂ − x₁)
The trick is consistency. Whatever you subtract on top, you must subtract in the same order on the bottom. If you do y₂ − y₁ on top, you must do x₂ − x₁ on the bottom. Mixing the order is the number one reason students get the right number with the wrong sign.
How to Find Slope from a Graph
- Pick two points on the line where it crosses grid intersections perfectly.
- Count the rise — how many units you move up or down.
- Count the run — how many units you move left or right.
- Write it as a fraction: rise over run, then simplify.
If the line climbs as you read left to right, the slope is positive. If it falls, the slope is negative.
How to Find Slope from a Table
Tables hide the graph, but the math is identical. Choose any two rows, subtract the y-values, and divide by the difference of the matching x-values Still holds up..
Practice Problems with Answers and Work Shown
Try these on your own first, then compare And that's really what it comes down to..
Problem 1: Find the slope of the line through (2, 3) and (5, 9) Small thing, real impact..
m = (9 − 3) / (5 − 2) = 6 / 3 = 2
Problem 2: Find the slope of the line through (−1, 4) and (3, −2).
m = (−2 − 4) / (3 − (−1)) = −6 / 4 = −3/2
Problem 3: A line passes through (0, 1) and (4, −1) Practical, not theoretical..
m = (−1 − 1) / (4 − 0) = −2 / 4 = −1/2
Problem 4: What is the slope of y = 5?
We're talking about a horizontal line. The rise is always 0, so the slope is 0 Which is the point..
Problem 5: What is the slope of x = −3?
This is a vertical line. The run is 0, and division by zero is impossible, so the slope is undefined Practical, not theoretical..
Problem 6: Use the table to find the slope.
| x | 1 | 3 | 5 |
|---|---|---|---|
| y |
