How do you do slope equations

Question

A line passes through the points​ A(n,4) and​ B(6,8) and is parallel to

y=2x-−5.

What is the value of​ n?

Answer 1

First, we know that if two lines are parallel, then they have the same slope. As a result, following the form of y=mx+b, where m is the slope and b is the y-intercept, we find that the slope of the given line is 2.

Following from our above statement, we know that the slope of the line passing through points A(n,4) and B(6,8) is 2 as well so we have y=2x+b. From here, we need to determine the value the y-intercept, b, and we solve for b by substituting B(6,8) into our equation: 8 = 2(6)+b which yields b = 8-12 = -4. Now, we have the equation of our line: y = 2x-4. Finally, we solve for n by substituting A(n,4) into our equation: 4 = 2(n)-4 which yields 8 = 2(n) so n=4.

We can also check this by verifying that the slope between points A and B is 2. If we use the slope formula: rise/run = (y_B - y_A)/(x_B-x_A) = (8-4)/(6-4) = 4/2 = 2 which shows that, indeed, our slope is 2.