Question

A line contains the points (-3, 4) and (7, -1). Calculate the equation of the line in the form

Answer 1

Answer:

$y=-\frac{1}{2}x+\frac{5}{2}$

Step-by-step explanation:

First we need to find the slope of the line.  We can plug in both coordinates in to the slope formula.

The slope formula is:

$m=\frac{y2-y1}{x2-x1}$

So I will use (-3,4) as the first coordinate, and (7,-1) as the second coordinate.

x₁ = -3

y₁ = 4

x₂ = 7

y₂= -1

I will plug in these values to find the slope.

$m=\frac{y2-y1}{x2-x1}\\\\m=\frac{-1-4}{7-(-3)}\\\\m=\frac{-5}{10}\\\\m=-\frac{1}{2}$

Now that we know the slope is -1/2, we can plug in the slope and a point into the point slope equation.  Then we can solve for y.

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

I have attached an image of what this graph should look like.  Since the slope is -1/2, the y value should decrease by 1/2 every time you move over by 1 on the x axis.  And since the equation says "+5/2" we know we have to shift the graph up by 5/2.  The y-intercept will be 5/2.

I added another image that shows how to graph an equation using the equation y=mx+b