What is the slope of a line that passes through the point (−1, 1) and is parallel to a line that passes through (3, 6) and (1, −2)?

Jun 24, 2016

$m = 4$ and its equation is $y = 4 x + 5$

Explanation:

Parallel lines have the same slope, so we have to find the slope of the line joining the given points first.

Slope = $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} \text{ "("subtract the y's")/"subtract the x's}$

$m = \frac{6 - \left(- 2\right)}{3 - 1} = \frac{8}{2} = 4$

The slope of the line parallel to this line is also 4.

We now know the slope and one point of the new line.
It's equation can be found using the formula

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

y - 1 = 4(x -(-1)

$y = 4 x + 4 + 1$

$y = 4 x + 5$