Question

Line k's equation is y =8/7 x - 3 Line l is perpendicular to line k and passes through the point (2,-15/4). Find an equation for line ( in both point-slope form and slope-intercept for I An equation for l in point-slope form is. An equation for l in slope-intercept form is

Answer 1

The equation for k is,

$y=\frac{8}{7}x-3$

Here slope is 8/7..

Since, line I is perpendicular to k, the slope of the line I is, -7/8.

The general line equation is,

$y=mx+b$

Here, m is the slope and b is the y intercept.

As the line passes through the points (2, -15/4), we have,

$\begin{gathered} -\frac{15}{4}=-\frac{7}{8}\times2+b \\ -\frac{15}{4}=-\frac{7}{4}+b \\ b=-\frac{15}{4}+\frac{7}{4}=-\frac{8}{4}=-2 \end{gathered}$

Thus, the equations are,

$y=-\frac{7}{8}x-2$

The point slope form is,

$y+\frac{15}{4}=-\frac{7}{8}(x-2)$