Question

What's an equation that the passes through (-6,4) and is parallel to y=1/2x+8

I have been trying to solve this for days now. Really need the help. Show work too.

Answer 1

By definition, if two lines share the same gradient, they are said to be parallel. So, we know for this equation, it must have a gradient of 1/2.

Now, since the point (-6, 4) passes through the line, we know it must satisfy the equation. Since we have a gradient/slope and a point, we can use the point-gradient form:


`y - y_1 = (1)/(2)(x - x_1)`, where
`(x_1, y_1)` represents the points being passed through.


`y - 4 = (1)/(2)(x + 6)`

`2y - 8 = x + 6`

`2y = x + 14`

`y = (1)/(2)x + 7`