Write the equation of the line.Through (9, -7), perpendicular to 5x + 4y = 17?

Question

Write the equation of the line.

Through (9, -7),
perpendicular to 5x + 4y = 17

Answer 1

In order to find the equation of the line perpendicular to the one described, you must find the slope of the line described, then multiply that slope by -1 and invert to get a slope that would be perpendicular. Then, you need to find the equation of the line through (9, -7). The equation of a line in slope-intercept form is: y = mx + b, where m is the slope and b is the y-intercept.

So:

5x + 4y = 17
4y = -5x + 17
y = (-5/4)x + 17/4

m = -5/4

So, the slope of a line perpendicular to this line is m = 4/5
Now, find the equation of the line. We have a point and the slope, all we need to find is the y-intercept, b:

y = mx + b
-7 = m * 9 + b
-7 = 4/5 * 9 + b
-7 = 36/5 + b
-7 - 36/5 = b
b = -7 - 36/5
b = -35/5 - 36/5
b = -71/5

Therefore, the equation of a line through (9, -7) with slope m = 4/5 is:

y = (4/5)x - 71/5

and if you multiply through by 5:

5y = 4x - 71

Answer 2

put the equation into slope-intercept form

y = (-5/4)x + 17/4

So the slope of the line is -5/4
the slope of a perpendicular line is -1/m = 4/5

So the line is:
y = (4/5)x + b

Use the point (9,-7) to find b
-7 = (4/5)9 + b
-35 = 36 + 5b
5b = -71 and b = -71/5

The perpendicular line is:
y = (4/5)x - 71/5
5y = 4x - 71