Question

Find the equations of each line from the given information through (2, 4) and (5,- 4) .

Answer 1

The equation of the line through the given points is;

`3y\text{ = -8x + 28}`

Here, we want to get the equation of the line that passes through the given points

Generally, we have the equation of a line as;

`y\text{ = mx + b}`

where m represents the slope and b represents the y-intercept

To find the slope, we use the slope formula which is as follows;

`\begin{gathered} m\text{ = }(y_2-y_1)/(x_2-x_1) \\ \\ (x_1,y_1)\text{ = (2,4)} \\ (x_2,y_2)\text{ = (5,-4)} \\ \\ m\text{ = }(-4-4)/(5-2)\text{ = }(-8)/(3) \end{gathered}`

Partially, we have the complete equation as;

`y\text{ = }(-8)/(3)x\text{ + b}`

To get b, we use any of the points

Let us use the first point

`\begin{gathered} 4\text{ = }(-8)/(3)(2)\text{ + b} \\ 4\text{ = }(-16)/(3)+\text{ b} \\ \\ b\text{ = 4 + }(16)/(3)\text{ = }(12+16)/(3)\text{ = }(28)/(3) \end{gathered}`

So, the equation of the line is;

`y\text{ = }(-8)/(3)x\text{ + }(28)/(3)`

Multiply through by 3, we have;

`3y\text{ = -8x + 28}`