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 valueof the slope and the values of x and y using the coordinates of the given point, then determine the value of bUsing the above technique, find the ouation of the line containing the points (-2,14) and (4,- 1).

Answer 1

Step 1

Given;

`\begin{gathered} \text{The equation of the line contains the points;} \\ (-2,14)\text{ and(4,-1)} \end{gathered}`

Required; To find the equation of the line

Step 2

State the equation of a line in slope-intercept form

`\begin{gathered} y=mx+b_{} \\ \text{where, } \\ m=\text{slope} \\ b=\text{ y-intercept} \end{gathered}`

The slope of a line is given as;

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ y_2=-1 \\ y_1=14 \\ x_2=4 \\ x_1=-2 \end{gathered}`
`m=(-1-14)/(4-(-2))=(-15)/(4+2)=-(15)/(6)=-(5)/(2)`

Step 3

Find the required equation

`\begin{gathered} \text{The equation of the line becomes;} \\ y=-(5)/(2)x+b \\ y=14 \\ x=-2 \\ 14=-(5)/(2)(-2)+b \\ 14=5+b \\ b=\text{ 14-5} \\ b=9 \end{gathered}`

Hence, the equation will be written as;

`y=-(5)/(2)x+9`