# How do you write an equation in slope intercept form given that the line passes through the points (1,5) and (0,0)?

Jun 20, 2015

$y = 5 x + 0$

#### Explanation:

First calculate the slope.

If a line passes through two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ then its slope $m$ is (change in $y$) / (change in $x$), given by the formula:

$m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

To avoid negative values, I will swap the order of the two points given in the question, and let $\left({x}_{1} , {y}_{1}\right) = \left(0 , 0\right)$ and $\left({x}_{2} , {y}_{2}\right) = \left(1 , 5\right)$

Then:

$m = \frac{5 - 0}{1 - 0} = \frac{5}{1} = 5$

So the equation of the line in slope-intercept form must be:

$y = 5 x + c$

for some constant $c$ - which is the $y$ coordinate of the intercept with the $y$ axis.

This equation of the line must be satisfied by any point on the line, so we have:

${y}_{1} = 5 {x}_{1} + c$

That is:

$0 = \left(5 \cdot 0\right) + c$

So $c = 0$ and the equation of the line can be written:

$y = 5 x + 0$