Question

Write the equation of the line given points (-4,6) and (-8,10)

Answer 1

Answer:

the equation of the line in slope-intercept form is: $y=-x+2$

Step-by-step explanation:

First start by finding the slope of the segment that joins those two points using the general formula for the slope of the segments between two points $(x_1,y_1)$ and $(x_2,y_2)$ on the plane:

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

Then for our case, calling (-4, 6) = $(x_1,y_1)$ and (-8, 10) = $(x_2,y_2)$, we have:

$Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{10-6}{-8-(-4)}\\Slope=\frac{4}{-8+4}\\Slope=\frac{4}{-4}\\Slope= -1$

Now, knowing this, we can find the equation of the line by using the "point-slope" form of a line [of slope "m" and going through the point $(x_0,y_0)$ that tells us:

$y-y_0=m(x-x_0)$

We will be then using the found slope (-1) and for example one of the given points: (-4 , 6), thus:

$y-y_0=m(x-x_0)\\y-6=-1(x-(-4))\\y-6=-1(x+4)\\y-6=-x-4\\y=-x-4+6\\y=-x+2$