Question

Find the equation for the line that passes through the point (-4,1), and that is perpendicular to the line with the equation

Answer 1

`y=(4)/(3)x+(19)/(3)`

Step-by-step explanation

Given:

Point ( - 4, 1)

⇒x = -4 and y = 1

Perpendicular equation

3/4 x + y = -5/4

We need to re-write the above equation in the form y = mx + b

y = -3/4 x -5/4

Compare the above with y=mx + b where m is the slope and b is the intercept.

slope(m) = -3/4

Slope of vertical lines are inverse of one another.

This implies that the slpe of our new equation is:

`m=(-1)/(m)=(-1)/(-(3)/(4))=(4)/(3)`

Next, is to find the intercept of the new equation.

We can find this by substituting m = 4/3 , x = -4 and y = 1 into y=mx + b and then solve for b.

That is;

`\begin{gathered} 1=(4)/(3)(-4)+b \\ \\ 1=-(16)/(3)+b \\ \\ 1+(16)/(3)=b \\ \\ b=(3+16)/(3) \\ \\ b=(19)/(3) \end{gathered}`

We can proceed to form the new equation by simply substituting the values of m and b into y=mx + b

Hence, the equation is:

`y=(4)/(3)x+(19)/(3)`