MHB Find an equation of the line that is perpendicular to x - y + 2 = 0

[mathdad]

Find an equation of the line that is perpendicular to x - y + 2 = 0 and passes through the point (3,1). Write your answer in two forms: y = mx + b and Ax + By + C = 0.

The equation we want is perpendicular to the given equation. This means the slope must be the negative reciprocal of the slope of the given equation.

True?

Steps:

1. Solve the given equation for y.

2. Find the negative reciprocal slope of the equation in step 1.

3. Plug the slope from step 2 and the point (3,1) into the point-slope formula and solve for y.

4. Express the equation in the form Ax + By + C = 0

Correct?

 

[Greg]

For step 3, don't you mean "solve for b" instead of "solve for y"? (Wondering)

Other than that detail, I am in agreement with what you have posted. :)

 

[mathdad]

For step 3, don't you mean "solve for b" instead of "solve for y"? (Wondering)

Other than that detail, I am in agreement with what you have posted. :)

Why solve for b in step 3? The slope m is required for the needed equation not the y-intercept or b.

 

[Greg]

Sorry; I mistook "point-slope" for "slope-intercept". At any rate, I don't see why you'd use point-slope when slope-intercept and standard form are required. Also, slope-intercept seems easier to work with.

 

[mathdad]

Cool.

 

[mathdad]

Steps:

1. Solve the given equation for y.

x - y + 2 = 0

x - y = - 2

- y = - x - 2

y = (- x - 2)/(-1)

y = x + 2

2. Find the negative reciprocal slope of the equation in step 1.

The negative reciprocal of 1 is - 1. This is our slope.

3. Plug the slope from step 2 and the point (3,1) into the point-slope formula and solve for y.

y - 1 = -(x - 3)

y - 1 = - x + 3

y = - x + 3 + 1

y = - x + 4

4. Express the equation in the form Ax + By + C = 0.

x + y - 4 = 0