Answer:
[tex]y=-\frac{5}{3}x+20[/tex]
Here, m=-5/3, and b=y-intercept=20
Here, the y-intercept is: 20
Thus, option (d) is true.
Step-by-step explanation:
Given the equation
[tex]y=\frac{3}{5}x+10[/tex]
comparing the equation with the slope-intercept form
[tex]y=mx+b[/tex]
Here,
so the slope of the line is 3/5.
As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so
The slope of the perpendicular line will be: -5/3
Therefore, the point-slope form of the equation of the perpendicular line that goes through (15,-5) is:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-\left(-5\right)=\frac{-5}{3}\left(x-15\right)[/tex]
[tex]y+5=\frac{-5}{3}\left(x-15\right)[/tex]
simplifying the equation to convert it into the slope-intercept form
We know that the slope-intercept form of the line equatio is
[tex]y=mx+b[/tex]
here 'm' is the slope and 'b' is the y-intercept
[tex]y+5=\frac{-5}{3}\left(x-15\right)[/tex]
subtract 5 from both sides
[tex]y+5-5=\frac{-5}{3}\left(x-15\right)-5[/tex]
[tex]y=-\frac{5}{3}x+20[/tex]
Here, m=-5/3, and b=y-intercept=20
Here, the y-intercept is: 20
Thus, option (d) is true.
