Question

Find the equation of the line that goes through the point ( 6, 5) and has a slope of 1/3

Answer 1

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

$y = \frac{1}{3} x +3$

Step-by-step explanation:

Since we already know a point the line intersects and its slope, we can use the point-slope formula $y-y_1 = m (x-x_1)$ to write an equation, then convert it to slope-intercept form.

Substitute values for $m$, $x_1$, and $y_1$. Since $m$ represents the slope, substitute $\frac{1}{3}$ in its place. Since $x_1$ and $y_1$ represent the x and y values of one point the line intersects, use the x and y values of (6,5) and substitute them into the equation. Substitute 6 for $x_1$ and 5 for $y_1$. Then, isolate y to put it into slope-intercept form and find an answer:

$y -5 = \frac{1}{3} (x-6)\\y-5 = \frac{1}{3}x-2\\y = \frac{1}{3} x+3$