Respuesta :
Answer:
Point-slope form of equation of a line that passes from (-1,3) and (0,0) is given as y-3=-3(x+1).
Slope-intercept form of equation is given as y=-3x.
Step-by-step explanation:
In the question, it is given that the line passes from (-1,3) and (0,0).
It is asked to write the point-slope form of the equation and rewrite it as slope-intercept form.
Step 1 of 2
Passing point of line is (-1,3).
Hence, [tex]$x_{1}=-1$[/tex] and
[tex]$y_{1}=3 \text {. }$[/tex]
Also, Passing point of line is (0,0).
Hence, [tex]$x_{2}=0$[/tex] and
[tex]$y_{2}=0 \text {. }$[/tex]
Substitute the above values to find the slope of line which is given by [tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
[tex]$\begin{aligned}m &=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\m &=\frac{0-3}{0-(-1)} \\m &=\frac{-3}{1} \\m &=-3\end{aligned}$[/tex]
Hence, slope of the line is -3
Step 2 of 3
It is obtained that m=-3
[tex]$y_{1}=3$[/tex]
and [tex]$x_{1}=-1$[/tex]
Substitute the above values in point-slope form of equation given by [tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]
[tex]$y-y_{1}=m\left(x-x_{1}\right)$\\ $y-3=-3(x-(-1)$\\ $y-3=-3(x+1)$[/tex]
Hence, point-slope form of equation given as y-3=-3(x+1).
Step 3 of 3
Solve y-3=-3(x+1) to write it as slope-intercept form given by y=mx+c
[tex]$y-3=-3(x+1)$\\ $y-3=-3 x-3$\\ $y=-3 x-3+3$\\ $y=-3 x$[/tex]
Hence, slope-intercept form of equation is given as y=-3x.
