Answer:
y = [tex]\frac{1}{2}x + \frac{29}{4}[/tex]
Step-by-step explanation:
First, we need to rearrange the equation to make it y = mx + c
4x - y = 3
y + 3 = 4x
y = 4x -3
So the slope of the line is 4.
The slope of a line perpendicular to an equation is:
[tex]\frac{-1}{gradient}[/tex]
So the slope of the perpendicular line is:
[tex]\frac{-1}{4}[/tex] = -0.25
Now to find the equation of a line you can use the following equation:
y - y₁ = m(x - x₁)
Where y₁ is the y-coordinate, x₁ is the x-coordinate and m is the gradient. Plug the values in:
y₁ = 6
x₁ = -5
m = [tex]\frac{-1}{4}[/tex]
y - 6 = [tex]\frac{-1}{4}[/tex](x - - 5)
To get rid of the fraction we need to multiply the whole equation by 4:
4y - 24 = -1(x - - 5)
The two negatives cancel out:
4y - 24 = -1(x + 5)
Multiply the brackets out:
4y - 24 = -x + 5
Now, to rearrange the formula back into y = mx + c
Move the -24 over to the other side making it a +24:
4y = 2x + 5 + 24
4y = 2x + 29
Divide everything by 4:
y = [tex]\frac{2}{4}x + \frac{29}{4}[/tex]
y = [tex]\frac{1}{2}x + \frac{29}{4}[/tex]
