Find the Line Equation Passing Through (0, -6) and (4, 0)

A straight line is drawn forming a triangle with the x and y axes.

The line passes through the points $(0,-6),(4,0)$.

Choose the equation that represents the line.

Let's derive the equation of the line:

• Step 1: Calculate the Slope
  The slope $m$ of a line through two points $(x_1, y_1)$ and $(x_2, y_2)$ is computed as follows: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the given points $(0, -6)$ and $(4, 0)$: $m = \frac{0 - (-6)}{4 - 0} = \frac{6}{4} = \frac{3}{2}$ Hence, the slope of the line is $\frac{3}{2}$.

• Step 2: Write the Equation Using the Slope-Intercept Form
  The slope-intercept form is: $y = mx + b$ Where $m$ is the slope and $b$ is the y-intercept. Since the line passes through $(0, -6)$, this point is the y-intercept ($b = -6$). Thus, we have: } $y = \frac{3}{2}x - 6$

Therefore, the equation of the line is $y = \frac{3}{2}x - 6$.

The correct choice is option 4.