Question

Find the equation (in terms of x ) of the line through the points (-4,5) and (2,1)y=

Answer 1

Given:

There are given that the two points are:

$(-4,5)\text{ and }(2,1)$

Explanation:

To find the equation, first, we need to find the slope of the line from the given points.

So,

From the formula of slope:

$m=\frac{y_2-y_1}{x_2-x_1}$

Where,

$x_1=-4,y_1=5,x_2=2,y_2=1$

Then,

Put all the values into the above formula:

So,

$\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{1-5}{2+4} \\ m=-\frac{4}{6} \\ m=-\frac{2}{3} \end{gathered}$

Now,

From the formula of point-slope form:

$y-y_1=m(x-x_1)$

Then,

$\begin{gathered} y-y_{1}=m(x-x_{1}) \\ y-5=-\frac{2}{3}(x-(-4)) \\ y-5=-\frac{2}{3}(x+4) \\ 3y-15=-2(x+4) \end{gathered}$

Then,

$\begin{gathered} 3y-15=-2(x+4) \\ 3y-15=-2x-8 \\ 3y-15+2x+8=0 \\ 3y+2x-7=0 \\ 3y=-2x+7 \\ y=-\frac{2}{3}x+\frac{7}{3} \end{gathered}$

Final answer:

Hence, the equation of line is shown below:

$y=-\frac{2}{3}x+\frac{7}{3}$