Respuesta :
Answer:
Point-slope form: y + 2 = -5(x - 7)
Slope-intercept form: y = -5x + 33
Explanation:
Two lines are perpendicular if their slope multiplies to -1. So, we can find the slope of our equation as:
[tex]\begin{gathered} m\times\frac{1}{5}=-1 \\ m\times\frac{1}{5}\times5=-1\times5 \\ m=-5 \end{gathered}[/tex]Because the slope of the line y = 1/5x + 2 is 1/5, the number beside the x.
Now, we write the equation of a line in a point-slope form as:
[tex]y-y_1=m(x-x_1)[/tex]Where m is the slope and (x1, y1) are the coordinates of a point. So, replacing m = -5 and (x1, y1) by (7, -2), we get:
[tex]\begin{gathered} y-(-2)=-5(x-7) \\ y+2=-5(x-7) \end{gathered}[/tex]Now, to write the equation in slope-intercept form, we need to solve for y, so:
[tex]\begin{gathered} y+2=-5(x)-5(-7) \\ y+2=-5x+35 \\ y+2-2=-5x+35-2 \\ y=-5x+33 \end{gathered}[/tex]Therefore, the answers are:
Point-slope form: y + 2 = -5(x - 7)
Slope-intercept form: y = -5x + 33
