What is the equation of the line that is parallel to the graph of y = 2x - 5 and passes through the point (8, 10)?

Answer 1

The line that is parallel to this line will have the same slope of this line, as the two will never intersect. They will run side by side. The line y = 2x - 5 is written in slope-intercept form, which is y = mx + b. The value of m represents the slope, and in this equation m = 2. Therefore, the line we are looking for will have a slope of 2 also.

That line should also be in slope-intercept form. We now know the value of m, but we also know the value of x and y. The ordered pair (8, 10) is a point on the line, and every ordered pair is in the form (x, y). Therefore, x = 8 and y = 10. We can plug those values into y = mx + b, along with m = 2. That gives us:

10 = 2(8) + b We need to solve for b.

10 = 16 + b

b = -6

Hence, the line parallel to y = 2x - 5 with the given characteristics is y = 2x - 6.

Answer 2

Another way to solve is to use the point slope formula, still using the slope of 2 because of the parallel lines.

y - y₁ = m(x - x₁)

y - 10 = 2(x - 8)

y - 10 = 2x - 16

y = 2x - 6

Either way works!