slope-intercept form of an equation

Question

Write the slope-intercept form of an equation for the line that passes  through the given point and is perpendicular to the graph of the equation

 

1.

 (4, 7), 3y - 2x = -3

 

2.

(1, -3), y =   1/2  x + 4

Answer 1

1) The line equation 3y - 2x = - 3

Write the equation in slope intercept form y = mx + b

Where m is slope and  b is y intercept.

3y = 2x - 3

y = (2/3)x - 1

Slope = 2/3 y intercept is - 1.

We know that perpendicular lines slopes are negative reciprocal to each other.

So required line slope is -3/2.

Now, the line equation is y = (-3/2)x + b.

Find the y - intercept by substituting point in the line equation say (x, y) = (4, 7).

7 = (-3/2)4 + b

7 = - 6 + b

b = 7 + 6

b = 13

The line equation in slope - intercept - form is y = (-3/2)x + 13.

Answer 2

2) The line equation y = x/2 + 4

Compare it to slope intercept form y = mx + b

Where m is slope and  b is y intercept.

m = 1/2, b = 4

We know that perpendicular lines slopes are negative reciprocal to each other.

So required line slope is - 2.

Now, the line equation is y = - 2x + b.

Find the y - intercept by substituting point in the line equation say (x, y) = (1, -3).

- 3 = (-2)1 + b

- 3 = - 2 + b

b = - 3 + 2

b = - 1

The line equation in slope - intercept - form is y = - 2x - 1.