Answer (assuming it can be slope-intercept form):
[tex]y = \frac{1}{3} x +3[/tex]
Step-by-step explanation:
Since we already know a point the line intersects and its slope, we can use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] to write an equation, then convert it to slope-intercept form.
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{1}{3}[/tex] in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] 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 [tex]x_1[/tex] and 5 for [tex]y_1[/tex]. Then, isolate y to put it into slope-intercept form and find an answer:
[tex]y -5 = \frac{1}{3} (x-6)\\y-5 = \frac{1}{3}x-2\\y = \frac{1}{3} x+3[/tex]
