Question

Write the slope-intercept equation for the line that passes through (8, 12) and is perpendicular to -4x – 7y = 14

Answer 1

Formulas for indignant slope from a perpendicular line is m1x m2=-1
-7y=4x+14
Y=-4x-14 so m1= -4 so m2 will be -4x m=-1
m2=1/4
Y-12=1/4(x-8)

Answer 2

Solve -4x – 7y = 14 for y.\[y=-\frac{4 x}{7}-2 \]Let y = m x + b be the line equation to be determined. We know y and x because the line passes through the point (8,12). m is the negative of the reciprocal of the x coefficient. Plug in the previous values for x, y and m and solve for b:\[y=m x+b \]\[12=-\left(-\frac{4}{7}\right)^{-1} 8+b \]\[12=14+b \]\[b=2 \]\[y=-\left(-\frac{4}{7}\right)^{-1} x+2 \]\[y=\frac{7}{4} x+2 \]In the attached plot, the line above is colored red and -4x – 7y = 14 is colored blue.