Question

Passing through (-4,1) and parallel to the line whose equation is 5x-2y-3=0

Answer 1

`y=(5)/(2)x+11`

Explanation:

Convert to slope-intercept form

`5x-2y-3=0\\5x-3=2y\\y=(5)/(2)x-(3)/(2)`

Since the line that passes through (-4,1) must be parallel to the above function, then the slope of that function must also be 5/2:

`y-y_1=m(x-x_1)\\y-1=(5)/(2)(x-(-4))\\y-1=(5)/(2)(x+4)\\y-1=(5)/(2)x+10\\y=(5)/(2)x+11`

Therefore, the line
`y=(5)/(2)x+11` passes through (-4,1) and is parallel to the line whose equation is
`5x-2y-3=0`. I've attached a graph of both lines if it helps you better understand!