# How do you write an equation of a line given (0,4) & is parallel to y=3x-7?

Jul 10, 2016

$y = 3 x + 4$

#### Explanation:

To solve this problem, we'll need to use our friend the point slope formula. (You'll use this formula in more advanced math more often then you think!)

Point slope formula is: $y - {y}_{1} = m \left(x - {x}_{1}\right)$

${x}_{1}$ and ${y}_{1}$ are the x and y values for the coordinate it gives you and $m$ is your slope which is attained from the equation it gives.

If it's parallel to the line, then it must have an equal slope. The line is given in $y = m x + b$ form so we find that the slope (m) is 3.

Looking at our coordinates the x coordinate is 0 and the y coordinate is 4 so that gives us ${x}_{1} = 0$ and ${y}_{1} = 4$ which is all we need to finish the problem.

$y - 4 = 3 \left(x - 0\right)$

Now we solve for y by distributing the 3 on the right side and adding 4 to both sides.

$y = 3 x + 4$