Given the points (-1, 3) and (3, 5), what is the slope?

m=(5-3)/(3+1)

m=2/4

m=1/2

y=1/2x+b

5=3/2+b

b=7/2

y=(1/2)x+(7/2)

y-intercept is 7/2.

x-intercept is -7.

Check out my Math Variety blog posts on slope for an explanation of this term, practice problems, and solutions.

http://mathvariety.blogspot.com/2009/04/slope.html

http://mathvariety.blogspot.com/2009/05/slope-prac...

http://mathvariety.blogspot.com/2009/05/slope-solu...

Start with y=mx+b. This is slope intercept form. We'll change it to standard form later.

slope=m=change in y/change in x=(y2-y1)/(x2-x1); here, y2=5, y1=3, x2=3, x1= -1, so:

slope=(5-3)/(3-(-1))

slope=2/4=1/2=m

Now we have:

y=(1/2)x+b

Find b. Plug in either (x,y) point and solve for b. I'll use (3,5), so:

5=(1/2)(3)+b

5=(3/2)+b

b=7/2

The equation in slope intercept form is y=(1/2)x+(7/2). Subtract (1/2)x to get this in standard form:

(-1/2)x+y=(7/2)

Multiply by -2 to clear the fractions:

x-2y= -7 (answer in stanard form)

To find the y-intercept, plug in 0 for x and solve for y to get:

0-2y= -7

-2y= -7

y=7/2

So, the y-intercept is (0,7/2).

To find the x-intercept, plug in 0 for y and solve for x to get:

x-2(0)= -7

x-0= -7

x= -7

The x-intercept is (-7,0).

Slope: 2

y-intercept: (0, 5)

x-intercept: (-2.5, 0)

standard form: -2x + y = 5

I'm 99% sure I did everything right, but it's been awhile since I've done this math :)

slope = (5-3)/(3+1) = 1/2

y-5=1/2(x-3)

y= 1/2x+7/2

at y=0, x=-7

at x=0, y=7/2