Answer:
The final equation is [tex]y = \frac{4}{3}x - \frac{16}{3}[/tex]
Step-by-step explanation:
The slope of the line CB where, C(0,3) and B(12,-6) will be
[tex]M = \frac{- 6 - 3}{12 - 0} = - \frac{3}{4}[/tex]
Now, if the line perpendicular to the line CB has slope N, then M × N = - 1
⇒ [tex]N = \frac{4}{3}[/tex] {Since [tex]M = - \frac{3}{4}[/tex]}
Now, equation of the straight lines which are perpendicular to CB will be in slope-intercept form
[tex]y = \frac{4}{3}x + c[/tex] {Where, c is the y-intercept}
If this straight line passes through the point (7,4), then
[tex]4 = \frac{4}{3} \times 7 + c[/tex]
⇒ 12 = 28 + 3c
⇒ 3c = - 16
⇒ [tex]c = - \frac{16}{3}[/tex]
Therefore, the final equation is [tex]y = \frac{4}{3}x - \frac{16}{3}[/tex] (Answer)
