Question

Write a linear equation that passes through the points (3, 1) and (-2, 6). ELE BE CE EL PR ET EM BRE SHO This

Answer 1

The equation of the line in slope intercept form is;

`y=-x+4`

And the equation of the line in point-slope form is;

`y-1_{}=-1(x-3_{})`

Step-by-step explanation:

We want to write a linear equation that passes through the points;

`(3,1)\text{ and }(-2,6)`

Firstly, let us find the slope of the line;

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=(6-1)/(-2-3) \\ m=(5)/(-5) \\ m=-1 \end{gathered}`

So, we can now use the point-slope equation of line to find the equation of the line;

`y-y_1=m(x-x_1)_{}`

using the point given;

`(x_1,y_1)=(3,1)`

And the derived slope, we have;

`\begin{gathered} y-y_1=m(x-x_1)_{} \\ y-1_{}=-1(x-3_{}) \\ y-1=-x+3 \\ y=-x+3+1 \\ y=-x+4 \end{gathered}`

Therefore, the equation of the line in slope intercept form is;

`y=-x+4`

And the equation of the line in point-slope form is;

`y-1_{}=-1(x-3_{})`