Answer:
y = [tex]-\frac{2}{7}[/tex]x + 4[tex]\frac{6}{7}[/tex]
Step-by-step explanation:
We are to find the equation of line 1 which passes through point (-4,6)
Line 1 is perpendicular to line 2.
The equation of line 2 is; y = [tex]\frac{7}{2}[/tex]x + 5
The slope of line 2 is [tex]\frac{7}{2}[/tex]
Because the product of two perpendicular line is -1;
The slope of line 1 is -1 ÷ [tex]\frac{7}{2}[/tex] = [tex]\frac{-2}{7}[/tex]
Taking another point (x,y) on line 1;
Slope = change in y ÷ change in x
[tex]\frac{-2}{7}[/tex] = [tex]\frac{y - 6}{x - -4}[/tex]
y - 6 = [tex]\frac{-2}{7}[/tex](x + 4)
y - 6 = [tex]\frac{-2}{7}[/tex]x - [tex]\frac{8}{7}[/tex]
y = [tex]\frac{-2}{7}[/tex] - [tex]\frac{8}{7}[/tex] + 6
y = [tex]-\frac{2}{7}[/tex]x + 4[tex]\frac{6}{7}[/tex]
