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

Question

Abigail Allen · Accepted Answer

#y=3x+4#

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(x-x_1)#

#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=mx+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(x-0)#

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

#y=3x+4#

Avery Alexander · Answer

undefined To write the equation of a line parallel to $ y = 3x - 7 $ and passing through the point $ (0, 4) $, you use the same slope as the given line. The slope of $ y = 3x - 7 $ is 3. Therefore, the equation of the parallel line is $ y = 3x + b $. To find the value of $ b $, substitute the coordinates of the given point $ (0, 4) $ into the equation. So, $ 4 = 3(0) + b $. Solving for $ b $, you get $ b = 4 $. Hence, the equation of the parallel line is $ y = 3x + 4 $.

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

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