from the question;
we are to find the equation of line passing through the points (1, -8) and (4, 4)
first,
we need to define the formula of the equation of line passing through two points
the equation is given as
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}_{}[/tex]
from the two points
[tex]\begin{gathered} x_{1_{}}=1_{}_{} \\ y_1\text{ = -8} \\ x_2\text{ = 4} \\ y_2\text{ = 4} \end{gathered}[/tex]
substituting these values into the above equation, we get
[tex]\begin{gathered} \frac{y\text{ - (-8)}}{x\text{ - 1}}\text{ = }\frac{4\text{ - (-8)}}{4\text{ - 1}} \\ \frac{y\text{ + 8}}{x\text{ - 1}}\text{ = }\frac{4\text{ + 8}}{3} \\ \frac{y\text{ + 8}}{x\text{ - 1}}\text{ = }\frac{12}{3} \\ \frac{y\text{ + 8}}{x\text{ - 1}}\text{ = 4} \\ \text{cross multiply} \\ y\text{ + 8 = 4(x - 1)} \\ y\text{ + 8 = 4x - 4} \\ y\text{ = 4x - 4 - 8} \\ y\text{ = 4x - 12} \end{gathered}[/tex]
therefore the equation of line passing through the points (1, -8) and (4, 4)
is y = 4x - 12
