Write the equation of the line in slope-intercept form. Points are (0, -2) and (3, 0)

1 answer

To find the equation of the line in slope-intercept form \(y = mx + b\), we start by determining the slope \(m\) using the two points given: (0, -2) and (3, 0).

  1. Calculate the slope \(m\): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-2)}{3 - 0} = \frac{0 + 2}{3} = \frac{2}{3} \]

  2. Use one point to solve for the y-intercept \(b\). We can use the point (0, -2): \[ y = mx + b \rightarrow -2 = \frac{2}{3}(0) + b \rightarrow -2 = b \]

  3. Now we have both \(m\) and \(b\):

    • Slope \(m = \frac{2}{3}\)
    • Y-intercept \(b = -2\)
  4. Write the equation in slope-intercept form: \[ y = \frac{2}{3}x - 2 \]

Thus, the equation of the line in slope-intercept form is: \[ \boxed{y = \frac{2}{3}x - 2} \]