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.
