Slope and y-Intercept Practice Problems

What this problem type covers

Each problem gives two points with whole-number coordinates and asks for the slope and the y-intercept. Early bands have integer slopes; later ones have fractional slopes that must stay as reduced fractions.

Example problems

One example from each difficulty band, with worked solutions.

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1. 1 · ★1
   Find the slope and the y-intercept of the line through these two points.
   (−1, 7), (0, 4)
   • ①slope = 3, y-intercept = 4
   • ②slope = −1/3, y-intercept = 4
   • ③slope = −3, y-intercept = −4
   • ④slope = −3, y-intercept = 4
   • ⑤slope = −3, y-intercept = 7
   Show solution

   ④slope = −3, y-intercept = 4

   1. Slope = (y₂ − y₁) / (x₂ − x₁) = (4 − 7) / (0 − −1) = −3
   2. Substitute one point into y = mx + b: 7 = −3·(−1) + b, so b = 4
   3. The line is y = −3x + 4
   4. So slope = −3, y-intercept = 4
2. 2 · ★2
   Find the slope and the y-intercept of the line through these two points.
   (1, 0), (2, 5)
   • ①slope = 5, y-intercept = −5
   • ②slope = 1/5, y-intercept = −5
   • ③slope = 5, y-intercept = 5
   • ④slope = −5, y-intercept = −5
   • ⑤slope = 5, y-intercept = 0
   Show solution

   ①slope = 5, y-intercept = −5

   1. Slope = (y₂ − y₁) / (x₂ − x₁) = (5 − 0) / (2 − 1) = 5
   2. Substitute one point into y = mx + b: 0 = 5·(1) + b, so b = −5
   3. The line is y = 5x − 5
   4. So slope = 5, y-intercept = −5
3. 3 · ★3
   Find the slope and the y-intercept of the line through these two points.
   (−4, −4), (−3, −2)
   • ①slope = 2, y-intercept = 5
   • ②slope = −2, y-intercept = 4
   • ③slope = 2, y-intercept = −4
   • ④slope = 2, y-intercept = 4
   • ⑤slope = 1/2, y-intercept = 4
   Show solution

   ④slope = 2, y-intercept = 4

   1. Slope = (y₂ − y₁) / (x₂ − x₁) = (−2 − −4) / (−3 − −4) = 2
   2. Substitute one point into y = mx + b: −4 = 2·(−4) + b, so b = 4
   3. The line is y = 2x + 4
   4. So slope = 2, y-intercept = 4
4. 4 · ★4
   Find the slope and the y-intercept of the line through these two points.
   (−10, 24), (−8, 21)
   • ①slope = 3, y-intercept = 9
   • ②slope = −3/2, y-intercept = 9
   • ③slope = −3/2, y-intercept = −9
   • ④slope = −3/2, y-intercept = 24
   • ⑤slope = −2/3, y-intercept = 9
   Show solution

   ②slope = −3/2, y-intercept = 9

   1. Slope = (y₂ − y₁) / (x₂ − x₁) = (21 − 24) / (−8 − −10) = −3/2
   2. Substitute one point into y = mx + b: 24 = −3/2·(−10) + b, so b = 9
   3. The line is y = (−3/2)x + 9
   4. So slope = −3/2, y-intercept = 9
5. 5 · ★5
   Find the slope and the y-intercept of the line through these two points.
   (−3, −13), (0, −6)
   • ①slope = −7, y-intercept = −6
   • ②slope = 3/7, y-intercept = −6
   • ③slope = 7/3, y-intercept = −6
   • ④slope = 7/3, y-intercept = 6
   • ⑤slope = 7/3, y-intercept = −13
   Show solution

   ③slope = 7/3, y-intercept = −6

   1. Slope = (y₂ − y₁) / (x₂ − x₁) = (−6 − −13) / (0 − −3) = 7/3
   2. Substitute one point into y = mx + b: −13 = 7/3·(−3) + b, so b = −6
   3. The line is y = (7/3)x − 6
   4. So slope = 7/3, y-intercept = −6

Where people usually go wrong

• Inverting the slope formula. It is rise over run — (y₂ − y₁) / (x₂ − x₁), not the other way round.
• Subtracting the coordinates in a different order on top and bottom. Both differences must run from the same point to the same point, or the sign flips.
• Turning a fractional slope into a rounded decimal. 2/3 is exact; 0.67 is not the answer.
• Reading the y-intercept off one of the given points. The intercept is the y value at x = 0, which is usually neither point.
• Losing the sign of the intercept when rearranging y = mx + b.