Question 387244
The equation for slope-intercept form is:
y=mx+b
First, we need to find the slope for the original line.
We'll put the line into y=mx+b form:
-2x-7y=-14
-7y=2x-14
y={{{-2/7}}}x+2
Now, we have the slope of the original line. To find the perpendicular slope, we just find the negative reciprocal-- {{{7/2}}}
The new line has a slope, but no y intercept.
We'll plug in the values of x and y that have been supplied to find our 'b'.
y=mx+b
{{{-11=(7/2)*-8+b}}}
{{{-11=-28+b}}}
17=b
Therefore, b is 17
Finally, we know the perpendicular line's slope and y intercept. Therefore, we can make a slope intercept equation for the perpendicular line.
y=mx+b
y={{{7/2}}}x+17