Answer:
[tex]\boxed{y = -\dfrac{1}{2}x-6}}[/tex]
Step-by-step explanation:
The equation for a straight line is
y = mx + b
where m is the slope of the line and b is the y-intercept.
The line passes through the points (-12, 0) and (0, 6)
(a) Calculate the slope of the line
[tex]\begin{array}{rcl}m & =&\dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\ & = &\dfrac{6 - 0 }{0 - (-12)}\\\\& = &\dfrac{6}{-12}\\\\& = & -\dfrac{1}{2}\\\end{array}[/tex]
(b) Write the equation
The y-intercept is at x = -6.
[tex]\text{The equation for the line is $\boxed{\mathbf{y = -\dfrac{1}{2}x-6}}$}[/tex]
The diagram shows the graph of the line passing through the two intercepts.
