Answer:
[tex]y-7=\frac{8}{5}(x+5)[/tex]
or
[tex]y=\frac{8}{5} x +15[/tex]
Step-by-step explanation:
To write the equation, convert the line to slope intercept form to find the slope.
5x+8y=16
8y=16-5x
y=-5/8 x +2
The slope of this line is -5/8. The slope of the line perpendicular to this line will be the negative reciprocal or 8/5.
Write the equation using the slope m=8/5 and the point slope form.
[tex]y-y_1=m(x-x_1)\\y-7=\frac{8}{5}(x--5)\\y-7=\frac{8}{5}(x+5)[/tex]
This is the equation of the line. You can convert it to slope intercept form:
[tex]y-7=\frac{8}{5}(x+5)\\y-7 = \frac{8}{5}x + 8\\y=\frac{8}{5}x +15[/tex]
