Write an equation in slope intercept form for the line that goes through (4,3) and that is perpendicular to the line that goes through the points (-23,14) and (-31,-4)

The slope of the line that passes through the points (-23,14) and (-31,-4) is:

y₂-y₁/x₂-x₁

=-4-14/-31+23

=-18/-8

=9/4

The perpendicular line's slope is the negative reciprocal of the line's slope it is perpendicular to, which is -4/9. Now we have:

y=(-4/9)x+b

To solve for b, the y-intercept, we can substitute values for x and y in. Since this line passes through the point (4,3), we can substitute those values in.

3=(-4/9)(4)+b

3=-16/9+b

b=43/9

Therefore, the equation of the line is y=(-4/9)x+43/9.

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