Slope & the Forms of a Line — Drills
Slope & the Forms of a Line has 8 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 12 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Reciprocal — The flip of a fraction. The reciprocal of 35 is 53.
- Integer — A whole number, positive, negative, or zero.
- Coefficient — The number multiplying a variable — the 3 in 3n.
- Slope — How much y changes for each 1 that x increases.
- y-intercept — The output when x = 0 — where the line crosses the vertical axis.
- Distribute — Multiply a bracket out: 3(x + 4) = 3x + 12.
- Slope-intercept form — y = mx + b, with m the slope and b the y-intercept.
- x-intercept — The x value when y = 0 — where it crosses the x-axis.
- Point-slope form — y - y1 = m(x - x1). Best when you know a point and the slope.
- Standard form — Ax + By = C. Best for finding intercepts fast.
- Parallel — Same slope, different intercept.
- Perpendicular — Slopes multiply to -1 — negative reciprocals.
Point-slope form
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Write the equation of the line with slope 6 through (0, -4), in point-slope form.
Worked answer
y - -4 = 6(x - 0)
y + 4 = 6(x - 0)
Problem 2
Write the equation of the line with slope -7 through (-2, 6), in point-slope form.
Worked answer
y - 6 = -7(x - -2)
y - 6 = -7(x + 2)
Slope-intercept form
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Write y - 8 = 2(x - 1) in slope-intercept form.
Worked answer
y = 2x + 6
y - 8 = 2x - 2
y = 2x + 6
Problem 2
Write y + 1 = 4(x + 1) in slope-intercept form.
Worked answer
y = 4x + 3
y + 1 = 4x + 4
y = 4x + 3
Intercepts
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the x-intercept of 8x + 5y = 160.
Worked answer
20
8x = 160
x = 20
Problem 2
Find the x-intercept of 2x + 4y = 64.
Worked answer
32
2x = 64
x = 32
Parallel lines
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A line parallel to y = 4x + 1 has what slope?
Worked answer
4
m = 4
Problem 2
A line parallel to y = 4x - 2 has what slope?
Worked answer
4
m = 4
Perpendicular lines
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A line perpendicular to y = -87x + 1 has what slope?
Worked answer
7/8
Reciprocal of -87 is -78
Negated: 78
Check: -87 × 78 = -1 ✓
Problem 2
A line perpendicular to y = 13x + -1 has what slope?
Worked answer
-3
Reciprocal of 13 is 3
Negated: -3
Check: 13 × -3 = -1 ✓
From two points
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the equation of the line through (-1, 5) and (6, -30).
Worked answer
y = -5x + 0
m = -30 - (5)6 - (-1) = -5
5 = -5(-1) + b, so b = 0
y = -5x + 0
Problem 2
Find the equation of the line through (-5, 3) and (1, -3).
Worked answer
y = -1x - 2
m = -3 - (3)1 - (-5) = -1
3 = -1(-5) + b, so b = -2
y = -1x - 2
Special cases
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
What is the equation of the horizontal line through (7, 2)?
Worked answer
y = 2
y = 2
Problem 2
What is the equation of the vertical line through (-8, -1)?
Worked answer
x = -8
x = -8
Standard form
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Write y = 54x + 8 in standard form Ax + By = C with integer coefficients.
Worked answer
5x - 4y = -32
× 4: 4y = 5x - 32
5x - 4y = -32
Problem 2
Write y = 73x - 1 in standard form Ax + By = C with integer coefficients.
Worked answer
7x - 3y = 3
× 3: 3y = 7x + 3
7x - 3y = 3