Answer (assuming it can be in slope-intercept form):
[tex]y = \frac{2}{5} x[/tex]
Step-by-step explanation:
1) First, find the slope of the line using the slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. Substitute the x and y values of (0,0) and (5,2) into the formula and simplify like so:
[tex]m = \frac{2-0}{5-0} \\m = \frac{2}{5}[/tex]
So, the slope is [tex]\frac{2}{5}[/tex].
2) Now, use the point-slope formula to write the equation of the line. Using the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex], substitute values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex].
Since [tex]m[/tex] represents the slope, substitute [tex]\frac{2}{5}[/tex] in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] 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:
[tex]y-0=\frac{2}{5} (x-0)\\y = \frac{2}{5} x[/tex]
