Write the slope-intercept form of the equation of the line through the given points - Show Work and Explain

Question

Through: (4,2) and (-3,0)

Answer 1

Ok, this is a two step process. First we need to find the slope, then we use point-slope form to find the slope-intercept form.

 

Slope is found using both points. You can use them in either order, as long as you keep each ordered pair above each other, and the y values are on top.

 

m = y2 - y1

       ______

       x2 - x1

 

So we plug in:

m = 2 - 0

       ------

       4 - (-3)

 

You could also use this form - it makes no difference in the result of the slope:

m = 0 - 2

       ------

       -3 - 4

 

I like the top version because it keeps the fraction positive. The second one you would have to remember a negative divided by a negative is positive.

 

When we do the math, we get m = 2/7.

 

Now, we can use the point-slope formula to get to the slope-intercept form:

y - y1 = m(x - x1)

 

Leave x and y alone, and pick either of the two points to use as (x1,y1). I will pick (-3,0) as it will save us a step later on.

 

y - 0 = 2/7(x - (-3))

y-0 is the same as y, so I will drop the 0 from the equation from here on.

 

y = 2/7(x + 3) Negative times negative is positive.

Distribute the 2/7 through the right side, and we get:

 

y = 2/7x + 6/7 as our final answer.