Answer:
y=2x+6
Explanation:
Given any two points on a line, to find the equation of the line, we can use the two-point form of the equation of a line stated below.
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]If the points are:
[tex]\mleft(x_1_{},y_1\mright)=\mleft(-5,-4\mright),(x_2,y_2)=(-1,4)[/tex]Substitute into the formula:
[tex]\begin{gathered} \frac{y-(-4)}{x-(-5)}=\frac{4-(-4)}{(-1)-(-5)}\implies\frac{y+4}{x+5}=\frac{4+4}{-1+5}=\frac{8}{4} \\ \implies\frac{y+4}{x+5}=2 \end{gathered}[/tex]Next, we write it in the slope-intercept form:
[tex]\begin{gathered} y+4=2(x+5) \\ y=2x+10-4 \\ y=2x+6 \end{gathered}[/tex]The equation of the line is y=2x+6.
