find an equation of the line through (4,5) and parallel to y=4x+2

Answer 1

In linear equations (y = m(x) + b); the m is the slope, and the b is the y intercept.

for lines that are parallel, their slopes are the same (they never cross).

So, given y = 4x +2, we know the slope is 4, so the line that passes through (4,5) and is parallel will also have a slope of 4.

1. y = 4(x) + b
2. to solve the rest of the equation, you will use the points given (x,y), (4,5) and plug in the x and the y into the equation above to solve for b
3. 5 = 4(4) + b
4. 5 = 16 + b subtract 16 from both sides and this will give you b
5. -11 = b
6. to complete the equation, but your found "b" back into your equation
7. y = 4(x) -11 this is the equation of the line through (4,5) parallel to y =4x+2

I hope this helps you grasp the concept! :-)