Answer:
The equation of the line is.
[tex]y=-\frac{5}{2}x-4[/tex]
Step-by-step explanation:
Given:
The given points are (0, -4) and (-4, 6)
The equation of the line passing through the points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is.
[tex]\frac{x-x_{1}}{x_{2}-x_{1}}=\frac{y-y_{1}}{y_{2}-y_{1}}[/tex]
Thus, the equation of the line that passes through the points (0, -4) and (-4, 6) is
[tex]\frac{x-0}{(-4)-0}=\frac{y-(-4)}{6-(-4)}[/tex]
[tex]\frac{x}{-4}=\frac{y+4}{6+4}[/tex]
[tex]-\frac{x}{4}=\frac{y+4}{10}[/tex]
[tex]-\frac{10x}{4}=y+4[/tex]
[tex]-10x=4(y+4)[/tex]
[tex]-10x=4y+16[/tex]
[tex]4y=-10x-16[/tex]
The above equation is divided by 2 both sides.
[tex]2y=-5x-8[/tex]
[tex]y=-\frac{5}{2}x-4[/tex]
Therefore, the equation of the line that passes through the points (0, -4) and (-4, 6) is [tex]y=-\frac{5}{2}x-4[/tex]
