Question

Find the equation of the line that is parallel to y=1/2x-4 and contains the point (4,5)

Answer 1

y=(1/2)x+3

Explanation:

start with this equation. y=kx+a

then fill it in with k being your coefficient. you will not be able to get a yet. it should look like this.

5=(1/2)(4)+a

5=2+a

now solve

5-2=a

a=3

now to finish this off you need to make the equation which will be in the same format but without the x and y filled in.

y=(1/2)x+3

Answer 2

y = 1/2x + 3

Explanation:

The equation of a line that is parallel to another line has the same slope as the original line. The slope of the line y = 1/2x - 4 is 1/2. So, the slope of the line we are looking for is also 1/2.

The point-slope form of the equation of a line is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. Substituting the point (4,5) and the slope 1/2 into this equation, we get:

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

Solving for y, we get:

y = 1/2x + 3

So, the equation of the line that is parallel to y = 1/2x - 4 and contains the point (4,5) is y = 1/2x + 3.