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Lesson 52: Determining the Equation of a Line Given Two Points — Practice Questions

  1. 1. A line passes through the point $(-2, -5)$ and has a slope of $5$. Another point on this line is $(-1, \_\_\_)$.

  2. 2. A line has a slope of $-\frac{3}{4}$ and passes through the point $(4, 1)$. Which of the following is another point on the line?

    • A. (8, -2)
    • B. (0, 4)
    • C. (1, -3)
    • D. (7, 5)
  3. 3. To graph a line with slope $-2$ from point $(5, 8)$, you find a second point by moving down 2 units and right 1 unit. This second point has coordinates $(\_\_\_, 6)$.

  4. 4. When using the slope $m = -\frac{4}{7}$ to find a new point, what movements do the 'rise' and 'run' represent?

    • A. Go up 4 units and right 7 units.
    • B. Go down 4 units and right 7 units.
    • C. Go right 4 units and down 7 units.
    • D. Go down 4 units and left 7 units.
  5. 5. A line contains the point $(-3, 2)$ and has a slope of $\frac{1}{2}$. Using the rise and run, a second point on the line is $(\_\_\_, 3)$.

  6. 6. What is the slope of the line that passes through the points $(1, 2)$ and $(4, 11)$? $m$ = ___

  7. 7. Which equation represents the line passing through the points $(2, 5)$ and $(4, 9)$?

    • A. $y - 9 = 2(x - 4)$
    • B. $y - 5 = \frac{1}{2}(x - 2)$
    • C. $y - 9 = -2(x - 4)$
    • D. $y - 4 = 2(x - 9)$
  8. 8. A line passes through the points $(3, 1)$ and $(5, 7)$. When its equation is written in slope-intercept form, $y = mx + b$, what is the value of the y-intercept, $b$? $b$ = ___

  9. 9. What is the equation of the line that passes through the points $(1, 2)$ and $(4, 7)$?

    • A. $y - 2 = \frac{3}{5}(x - 1)$
    • B. $y - 7 = \frac{5}{3}(x - 4)$
    • C. $y - 7 = \frac{3}{5}(x - 4)$
    • D. $y - 1 = \frac{5}{3}(x - 2)$
  10. 10. Which of the following expressions is NOT a correct way to calculate the slope of the line passing through points $(x_1, y_1)$ and $(x_2, y_2)$?

    • A. $\frac{y_2 - y_1}{x_2 - x_1}$
    • B. $\frac{y_1 - y_2}{x_1 - x_2}$
    • C. $\frac{y_2 - y_1}{x_1 - x_2}$
    • D. $\frac{-(y_1 - y_2)}{x_2 - x_1}$