RANGER Math practice · Algebra · ages 13+
Free slope and y = mx + b practice
Ranger's Lab, the algebra world in Ranger's Math Trail, practices slope with a graph on every question: find the slope between two points, then pick the equation of the line through them in y = mx + b form. It also practices evaluating functions like f(x) = 2x² − 3x + 1.
The worked answer shows rise over run with the actual numbers, then finds b by putting one point into the equation.
Practice slope and linear equations now
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Free, no sign-up. The game asks your age once, then every answer comes with a hint and a step-by-step Show me how.
How to do it
- Slope m = (change in y) ÷ (change in x) = (y₂ − y₁) ÷ (x₂ − x₁).
- A positive slope goes up to the right; a negative slope goes down. A slope of 0 is flat.
- For y = mx + b, find m first, then put one point's x and y in and solve for b.
- To evaluate f(x) at a number, put that number in for every x and follow the order of operations.
Worked examples
Example 1What is the slope of the line through (2, −2) and (−2, 0)?
- Slope = (change in y) ÷ (change in x).
- Change in y: 0 − (−2) = 2. Change in x: −2 − 2 = −4.
- Slope = 2 ÷ (−4) = −1/2.
- Negative: the line goes DOWN to the right.
Answer: −1/2
Try one like it →Example 2f(x) = −2x2 + 5x − 3. What is f(−5)?
- f(−5) means: use x = −5.
- −2 × (−5)2 = −2 × 25 = −50.
- 5 × (−5) = −25.
- Total: −50 + (−25) + (−3) = −78.
Answer: −78
Try one like it →Mistakes to watch for
- Subtract in the same order on top and bottom: if you start with point 2 on top, start with point 2 on the bottom too.
- Simplify the slope: 4/6 is 2/3.
The game
Questions
How do I type a fraction slope like −2/3?
Use the − and / keys: −2/3. Any equal fraction counts, but simplifying is good practice.
What age is it for?
Slope comes in around grade 8 and Algebra 1 (ages 13 to 15). Adults brushing up can open every stop.
More math practice: Addition · Subtraction · Multiplication facts · Division and long division · Place value and rounding · Fractions · Decimals · Percents and ratios · Negative numbers · Order of operations · Exponents and square roots · Solving equations · Systems of equations · Factoring quadratics · Area, perimeter and volume · Angles · Pythagorean theorem · Circles · Mean, median, mode and range · All math topics