Question

Which of the following point-slope form equations could be produced with the points (2, -6) and (4, -3)?

Answer 1

Answer:

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

Step-by-step explanation:

       A line passes through the points $(2,-6)$ and $(4,-3)$.

To find the point-slope form of the line, we need a point on the line and the slope of the line.

As we have two points $(x_{1},y_{1})$ and $(x_{2},y_{2})$, the slope can be calculated as $\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$.

       Slope of the line = $\dfrac{-3-(-6)}{4-2}=\dfrac{3}{2}$

Given a line with slope $m$ and a point $(x_{1},y_{1})$, slope-point form is $y-y_{1}=m(x-x_{1})$

       Line is given by $y+6=\frac{3}{2}(x-2)$

∴ The line is given by $y+6=\frac{3}{2}(x-2)$