Question

Write an equation of a line that passes through the point (4,3) and is perpendicular to the graph of the equation y=−13x+4y

Answer 1

The equation of a line that passes through the point (x1,y1) and has a slope of m is
y-y1=m(x-x1)

slope of perpendicular lines mulitply to -1

so

y=-13x+4y
y=mx+b
m=slope
I think you meant -1/3, but ok

-13 times what=-1
what=1/13

(if yo meant -1/3, then the what=3)
given point (4,3)

for y=-13x+4y,
y-3=1/13(x-4)

for y=-1/3x+4y
y-3=3(x-4) or y=3x-9

Answer 2

First start by writing th equation y=mx+b then because we know the slope (m) is perpendicular to the other line we can find it. so it would be the negative reciprocal to -13 which is 1/13 then you can use the slope and the x and y point and sub them into the equation to find the b value
y=3 x=4 m=1/13
3=1/13*4+b then solve for b
3=4/13+b
3-4/13=b
2.69=b
the write out the equation
y=1/13x+2.69