Question

Find the equation for the line that is perpendicular to a line with the equation (y-1)=1/3x passing through the point (4,-3)

Answer 1

Answer:

y = -3x + 9

Step-by-step explanation:

We are asked to asked to find the equation of a line which is perpendicular to

y - 1 = 1/3x

Step 1: find the slope

y - 1 = 1/3x

y = 1/3x + 1

Slope m = 1/3x

Note: if two lines are perpendicular to the other, it is negative reciprocal to each other

m = -3/1

Step 2: using a point slope form

y - y_1 = m( x - x_1 )

Substitute m = -3/1

y - y_1 = -3( x - x _1)

Step 3: substitute the point

(4 , -3)

x_1 = 4

y_1 = -3

y - (-3) = -3/1( x - 4)

y + 3 = -3(x - 4)

Open the bracket

y + 3 = -3x + 12

Step 4: using a slope intercept form

y = mx + c

y + 3 = -3x + 12

y = -3x + 12 - 3

y = -3x + 9

The equation of the line is

y = -3x + 9