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

Answer:

The equation of the line in slope intercept form is;

$y=-x+4$

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

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

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;

$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{6-1}{-2-3} \\ m=\frac{5}{-5} \\ m=-1 \end{gathered}$

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;

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