Question

What is the equation of a line that passes through the points (1,-8) and (4,4)

Answer 1

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

`(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)_{}`

from the two points

`\begin{gathered} x_{1_{}}=1_{}_{} \\ y_1\text{ = -8} \\ x_2\text{ = 4} \\ y_2\text{ = 4} \end{gathered}`

substituting these values into the above equation, we get

`\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{ = }(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}`

therefore the equation of line passing through the points (1, -8) and (4, 4)

is y = 4x - 12