Question

What equation is parallel to y=-1/4x+5 and passes through (2,-3)

Answer 1

`(y+3)=-(1)/(4) (x-2)` (Point Slope Form)

OR

`y=-(1)/(4) x-(5)/(2)` (Slope Intercept Form)

Explanation:

Since we are looking for a parallel line, we know that the slope "m" must be equivalent to the slope of the line given in the problem (-1/4)

Given the point it passes through, we know that the point x = 2 and y = -3 exist on the line.

Now, we will use Point Slope Form (Below):

`(y-y_1)=m(x-x_1)`

Apply Point Slope Form:

`(y--3)=-(1)/(4) (x-2)`

Simplify:

`(y+3)=-(1)/(4) (x-2)`

This is your answer in Point Slope Form. Some instructors prefer students to evaluate their answers to slope-intercept form, so I will do that below. Both answers are equivalent and are thus valid.

Distribute -1/4:

`(y+3)=-(1)/(4) x+(1)/(2)`

Subtract 3 from both sides:

`y=-(1)/(4) x-(5)/(2)`

This is your answer in Slope Intercept Form. Again, both equations will present the same line if graphed.