Answer:
y+6=[tex]\frac{\textbf{3}}{\textbf{2}}[/tex](x-2)
Step-by-step explanation:
A line passes through the points [tex](2,-6)[/tex] and [tex](4,-3)[/tex].
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 [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex], the slope can be calculated as [tex]\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].
Slope of the line = [tex]\dfrac{-3-(-6)}{4-2}=\dfrac{3}{2}[/tex]
Given a line with slope [tex]m[/tex] and a point [tex](x_{1},y_{1})[/tex], slope-point form is [tex]y-y_{1}=m(x-x_{1})[/tex]
Line is given by [tex]y+6=\frac{3}{2}(x-2)[/tex]
∴ The line is given by [tex]y+6=\frac{3}{2}(x-2)[/tex]
