Find an equation for the line with the given properties. Express the equation in​ slope-intercept form.

Question

Containing the points P = (-4,4) and Q = (-3,2). What is the equation of the line? y =

Answer 1

(-4,4) and (-3,2) have a line through them with slope

= (4-2)/(-4- -3) = 2/(-4+3) = 2/-1 = -2

y=mx + b is slope intercept form

plug in m=-2

y =(-2)x + b to solve for b, the y intercept, plug in either point

4 = (-2)(-4) + b

b = 4-8 = -4

the line is

y=-2x -4 in slope intercept form

Answer 2

The equation of a line can be put in several different forms. The slope-intercept is one of those forms and it generically looks like y = mx + b where "m" is the slope and "b" is the y-intercept.

So we will be needing the slope. The slope is found using the slope equation:

where two points on the line are (x₁, y₁) and (x₂, y₂) so plugging in the points given to us (-4, 4) and (-3, 2), we get:

m = (2 - 4)/(-3 - -4) = (-2)/1 = -2

Now we can plug that value of "m" into y = mx + b to get y = -2x + b. The only thing left is to find the value of "b". Let's use one of the points given to us and plug it into "y = -2x + b" as an "x" and a "y". I'll pick the point (-4, 4). That gives us:

4 = -2(-4) + b

4 = 8 + b

-4 = b

So, plugging that value of "b" into y = -2x + b we get y = -2x - 4 which is our final answer.