Question

Find the equation of the line passing through the points (-3,14) and (2,-1). Write your final answer in slope-intercept form.

Answer 1

The slope-intercept form of a linear equation is given by:

`y=mx+b`

Where m is the slope and b is the y-intercept.

To calculate the slope, we can use the formula below with the given two points:

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1)\\ \\ m=(-1-14)/(2-(-3))\\ \\ m=(-15)/(5)\\ \\ m=-3 \end{gathered}`

Now, to find the value of b, let's use the point (2, -1) in the equation:

`\begin{gathered} y=mx+b\\ \\ -1=-3\cdot2+b\\ \\ -1=-6+b\\ \\ b=-1+6\\ \\ b=5 \end{gathered}`

Therefore the equation is y = -3x + 5.