Question

if the slope of a line and a point on the line are known the equation of the line can be found using the slope intercept form y=mx+b. to do so substitute the value of the slope and the values of x and y using the coordinates of the given point, then determine the value of b. using the above technique find the equation of the line containing the points (-8,13) and (4,-2).

Answer 1

`y\text{ =}(-5)/(4)x\text{ + 3}`

The general equation of a line is;

`y\text{ = mx + b}`

m is the slope and b is the y-intercept

To find the slope, we use the equation of the slope as follows;

`\begin{gathered} m\text{ = }(y_2-y_1)/(x_2-x_1) \\ \\ (x_1,y_1)\text{ = (-8,13)} \\ (x_2,y_2)\text{ = (4,-2)} \\ \\ m\text{ = }(-2-13)/(4-(-8))\text{ = }(-15)/(12)\text{ = }(-5)/(4) \end{gathered}`

We have the partial equation as;

`\begin{gathered} y\text{ = }(-5)/(4)x\text{ + b} \\ \\ \text{Substitute the point (-8,13)} \\ \text{x = -8 and y = 13} \\ \\ 13\text{ = }(-5)/(4)(-8)\text{ + b} \\ \\ 13\text{ = 10 + b} \\ b\text{ = 13-10 = 3} \end{gathered}`

We have the complete equation as;

`y\text{ =}(-5)/(4)x\text{ + 3}`