Given:
Given line passes through (-1,3) and (5, -5).
Required: Equation of the line
Explanation:
First, find the slope using the two point formula.
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{-5-3}{5-(-1)} \\ =\frac{-8}{6}=-\frac{4}{3} \end{gathered}[/tex]An equation of a line in slope-intercept form is y = mx+c, where m is the slope and c is the y-intercept.
Substitute the value of m into y = mx+c.
[tex]y=-\frac{4}{3}x+c...(1)[/tex]Plug the value (-1,3) into equation (1) to find c.
[tex]\begin{gathered} 3=-\frac{4}{3}(-1)+c \\ c=3-\frac{4}{3} \\ =\frac{5}{3} \end{gathered}[/tex]Substitute the obtained value of c into equation (1).
[tex]y=-\frac{4}{3}x+\frac{5}{3}[/tex]Final Answer:
[tex]y=-\frac{4}{3}x+\frac{5}{3}[/tex]