what is the point slope form of a line that passes through the point (2, 3) and has the same slope as y=5x+2

Answer 1

The equation y = 5x + 2 is in slope-intercept form, also known as y = mx + b. In this form "m" is the slope and "b" is the y-intercept (the number where the line crosses the y-axis) so we can read the slope right from the equation as 5.

The point-slope form of a line goes like this:

y - y₁ = m(x - x₁) where a point on the line is (x₁, y₁) and the slope of the line is "m". We are told that a point on the line is (2, 3) meaning x₁ = 2 and y₁ = 3. We know the slope is 5 (same as y = 5x + 2) sp we can plug in x₁, y₁, and "m":

y - 3 = 5(x - 2)

and that is the answer.