Respuesta :
We will find the x & y-intercepts as follows:
*First: We will calculate the slope:
[tex]m=\frac{-3-(-6)}{6-(-6)}\Rightarrow m=\frac{1}{4}[/tex]*Second: We will replace this slope and one of the points in the following expression:
[tex]y-y_1=m(x-x_1)[/tex]That is:
[tex]y-(-3)=(\frac{1}{4})(x-6)\Rightarrow y+3=\frac{1}{4}x-\frac{3}{2}[/tex][tex]\Rightarrow y=\frac{1}{4}x-\frac{9}{2}[/tex]*Third: We will find the x & y-components:
*x-component: We replace y = 0 and solve for x:
[tex]0=\frac{1}{4}x-\frac{9}{2}\Rightarrow\frac{1}{4}x=\frac{9}{2}\Rightarrow x=18[/tex]So, the x-intercept is located at (18, 0).
*y-intercept: We replace x = 0 and solve for y:
[tex]y=\frac{1}{4}(0)-\frac{9}{2}\Rightarrow y=-\frac{9}{2}[/tex]So, the y-intercept is located at (0, -9/2).
