Respuesta :
The point-slope form is as follows:
[tex]y-y_P=m(x-x_P)[/tex]Where m is the slope and (xP, yP) is a point on the line. We can use any opint as long as it is on the line.
The slope-intercept form is:
[tex]y=mx+b[/tex]Where m is the same slope and b is the y-intercept. We can find it by either using the y-intercept or by solving the slope-point form for y.
First, we need to find the slope using the points (4, -2) and (-8, 1):
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-(-2)}{-8-4}=\frac{1+2}{-12}=\frac{3}{-12}=-\frac{1}{4}[/tex]So, to find the point-slope form, we can use either points, so let's use (4, -2):
[tex]\begin{gathered} y-(-2)=-\frac{1}{4}(x-4) \\ y+2=-\frac{1}{4}(x-4) \end{gathered}[/tex]And to find the slope-intercept, we just solve the parenthesis and solve for y:
[tex]\begin{gathered} y+2=-\frac{1}{4}(x-4) \\ y+2=-\frac{1}{4}x+1 \\ y=-\frac{1}{4}x+1-2 \\ y=-\frac{1}{4}x-1 \end{gathered}[/tex]So, one of the possible point-slope forms is:
[tex]y+2=-\frac{1}{4}(x-4)[/tex]And the slope-intercept form is:
[tex]y=-\frac{1}{4}x-1[/tex]