Slope — Grade 7 Math, what it means and where it is taught
How much y changes for each 1 that x increases.
Taught in Grade 7 Math.
Where it is taught
What uses it later
This idea is needed for:
- Slope-intercept form — y = mx + b, with m the slope and b the y-intercept.
- Point-slope form — y - y1 = m(x - x1). Best when you know a point and the slope.
- Parallel — Same slope, different intercept.
- Perpendicular — Slopes multiply to -1 — negative reciprocals.
- Rate of change — The slope, in the units of the situation.
- Derivative — The slope of the tangent, written f'(x) or dydx.
- Difference quotient — f(x+h)-f(x)h, the slope over a gap of h.
Practise this idea
61 questions in the course bank use Slope, in Functions, Slope & Unit Rate, Linear Functions & y = mx + b, What Is a Function?, Systems of Linear Equations, Lines of Best Fit. The first 8 are below; the rest are in those units.
Problem 1
A table gives x = 0, 1, 2, 3 and y = 7, 11, 15, 19. What is the slope?
Worked answer
4
11 - 7 = 4, and the jump stays 4
Slope = 4
Problem 2
What is the slope of y = 4x + 1?
Worked answer
4
Slope = 4
Problem 3
A table gives x = 0, 1, 2, 3 and y = 7, 11, 15, 19. Find y when x = 10.
Worked answer
47
y = 4x + 7
4(10) + 7 = 47
Problem 4
A line passes through (2, 9) and (5, 21). Find its slope.
Worked answer
4
21 - 95 - 2 = 123 = 4
Problem 5
A line passes through (2, 9) and (5, 21). Find its y-intercept.
Worked answer
1
9 = 4(2) + b
9 = 8 + b, so b = 1
Check with (5,21): 20 + 1 = 21 ✓
Problem 6
Find the slope of the line through (1, 5) and (4, 14).
Worked answer
3
14 - 54 - 1 = 93 = 3
Problem 7
A table gives x = 1, 2, 3 and y = 5, 8, 11. Write the rule in the form mx+b.
Worked answer
3x+2
Jump is 3, so slope = 3
At x = 1, y = 5, so 3(1) + b = 5 and b = 2
y = 3x + 2
Problem 8
A line has slope -2 and passes through (3, 1). Find its y-intercept.
Worked answer
7
1 = -2(3) + b
1 = -6 + b
b = 7