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

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Answer 1 · 2015-06-20T07:42:39

$y = 5x + 0$

First calculate the slope.

If a line passes through two points $(x_1, y_1)$ and $(x_2, y_2)$ then its slope $m$ is (change in $y$ ) / (change in $x$ ), given by the formula:

$m = (Delta y)/(Delta x) = (y_2 - y_1) / (x_2 - x_1)$

To avoid negative values, I will swap the order of the two points given in the question, and let $(x_1, y_1) = (0, 0)$ and $(x_2, y_2) = (1, 5)$

Then:

$m = (5 - 0) / (1 - 0) = 5/1 = 5$

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

$y = 5x+c$

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:

$y_1 = 5x_1 + c$

That is:

$0 = (5*0) + c$

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

$y = 5x + 0$