Given:
The given line passes through (2,4) and (-6,-6)
Required: The 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{-6-4}{-6-2} \\ =\frac{-10}{-8} \\ =\frac{5}{4} \end{gathered}[/tex]The slope-intercept form of a line is of the form y = mx+c, where m is the slope and c is the y-intercept.
Substitute the obtained value of m into y = mx+c.
[tex]y=\frac{5}{4}x+c[/tex]Plug the point (2, 4) into the equation to find c.
[tex]\begin{gathered} 4=\frac{5}{4}\cdot2+c \\ c=4-\frac{5}{2} \\ =\frac{3}{2} \end{gathered}[/tex]Substitute the value of c into y = (5/4)x+c.
[tex]y=\frac{5}{4}x+\frac{3}{2}[/tex]Final Answer:
[tex]y=\frac{5}{4}x+\frac{3}{2}[/tex]