What is the equation of the line that is parallel to y = 4x + 3 and goes through the point (5, 9)?

Answer 1

Lines that are parallel have the same slope but different rate of changes. Think you and your friends age. You age at the same rate, but have different starting points. Therefore, you will never be the same age.

Y =mx+b

To write the equation of a line, we need m = slope and b = y intercept

So we know the slope (m) = 4, but we need to know the Y intercept. (b)

But we are given another point! Let's plug it in to find B.

9 = 4(5) + b = 9 = 20 + b b= -11

So Y = 4x -11

Hope this helps!

Answer 2

Parallel lines have the same slope. So the equation of the new line will have the same slope as y=4x+3:

m = 4

We also have a point in the new line:

(5, 9)

So, we can use the Point-slope form to find the equation of the line:

y - y₁ = m (x - x₁)

Substituting:

y - 9 = 4 (x - 5)

y - 9 = 4x - 20

y = 4x - 20 + 9

y = 4x - 11

The equation of the new line is y = 4x - 11