Answer: [tex]y + 1 = \frac{4}{3}\left(x - 3\right)\\\\[/tex]
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Explanation:
The given slope is [tex]m = \frac{4}{3}[/tex] and the line goes through the point [tex](x_1,y_1) = (3,-1)[/tex]
This means [tex]x_1 = 3 \ \text{ and } \ y_1 = -1[/tex]
We will plug this information into the point-slope formula below and simplify.
[tex]y - y_1 = m\left(x - x_1\right)\\\\y - (-1) = \frac{4}{3}\left(x - 3\right)\\\\y + 1 = \frac{4}{3}\left(x - 3\right)\\\\[/tex]
We stop here since your teacher wants the answer in point-slope form. As the name implies, point-slope form is very handy to quickly spot the slope and a point on the line.
If your teacher wanted the answer in slope-intercept form, then you'd solve for y to get it into y = mx+b form.
