Question

What is an equation of the line that passes through the points (0,0) and (5,2)

Answer 1

Answer (assuming it can be in slope-intercept form):

$y = \frac{2}{5} x$

Step-by-step explanation:

1) First, find the slope of the line using the slope formula,  $m = \frac{y_2-y_1}{x_2-x_1}$. Substitute the x and y values of (0,0) and (5,2) into the formula and simplify like so:

$m = \frac{2-0}{5-0} \\m = \frac{2}{5}$

So, the slope is $\frac{2}{5}$.

2) Now, use the point-slope formula to write the equation of the line. Using the point-slope formula $y-y_1 = m (x-x_1)$, substitute values for $m$, $x_1$, and $y_1$.

Since $m$ represents the slope, substitute $\frac{2}{5}$ in its place. Since $x_1$ and $y_1$ represent the x and y values of a point the line intersects, we can substitute the x and y values of one of the given points (I chose (0,0)) into the formula as well. Then, isolate y to put in slope-intercept form:  

$y-0=\frac{2}{5} (x-0)\\y = \frac{2}{5} x$