Question

What is the equation, in slope-intercept form, of the line that is perpendicular to the line

Answer 1

Answer:

$y=\frac{3}{2}x +1$

Step-by-step explanation:

We are given;

The equation of a line;

$y-4 = -\frac{2}{3}(x-6)$

We are required to determine the equation of a line perpendicular to the above line and passing through (-2, -2).

• We can get the gradient of a line when given its gradient and a point where it is passing through.

• In this case;

We need to know that the product of gradient of two parallel lines is -1

• Therefore, we can get the gradient of the unknown line;

m₁× m₂ = -1

Thus;

m₂ = -1 ÷ -2/3

     = 3/2

Thus, the gradient is 3/2 and the line passes through (-2,-2)

Thus, to get its equation, we take another point (x,y)

We get;

$\frac{y+2}{x+2}= \frac{3}{2}$

Then;

$2(y+2)=3(x+2\\2y + 4 = 3x + 6$

Combining the like terms,

$2y=3x+2$

In the form of slope-intercept;

$y=\frac{3}{2}x +1$