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Lesson 4: Construct Functions to Model Linear Relationships — Practice Questions

  1. 1. A line crosses the y-axis at $(0, 2)$ and passes through the point $(5, 12)$. What is the slope, $m$, of the line? The slope is ___.

  2. 2. A line has a y-intercept at $(0, 1)$ and passes through the point $(6, 4)$. Which equation represents this line in slope-intercept form?

    • A. $y = 2x + 1$
    • B. $y = \frac{1}{2}x + 1$
    • C. $y = \frac{1}{2}x + 6$
    • D. $y = x + \frac{1}{2}$
  3. 3. The graph of a linear equation crosses the y-axis at the point $(0, -4)$. The y-intercept, $b$, of this equation is ___.

  4. 4. A line passes through the points $(0, 6)$ and $(2, 0)$. What is the equation of the line?

    • A. $y = 3x + 6$
    • B. $y = -3x + 2$
    • C. $y = -3x + 6$
    • D. $y = -\frac{1}{3}x + 6$
  5. 5. A line has a y-intercept at $(0, -5)$ and passes through $(2, -1)$. For the equation $y = mx + b$ representing this line, the value of $m$ is ___.

  6. 6. A line has a slope of -2 and passes through the point (3, 7). Write the equation of the line in slope-intercept form. $y = \_\_\_$

  7. 7. What is the equation of the line that passes through the points $(2, 5)$ and $(5, 14)$?

    • A. $y = 3x - 1$
    • B. $y = 3x + 1$
    • C. $y = \frac{1}{3}x + \frac{13}{3}$
    • D. $y = -3x + 11$
  8. 8. A linear function has a slope of 5 and passes through the point $(-2, -4)$. The y-intercept of the function is ___.

  9. 9. What is the slope of the line that passes through the points $(-1, 8)$ and $(3, -4)$? The slope is ___.

  10. 10. If $f$ is a linear function with $f(2) = 10$ and $f(5) = 1$, which equation represents the function?

    • A. $f(x) = 3x + 4$
    • B. $f(x) = -3x + 4$
    • C. $f(x) = -3x + 16$
    • D. $f(x) = -\frac{1}{3}x + \frac{32}{3}$