What is the slope-intercept form equation of the line that passes through (1, 3) and (3, 7)?

y = −2x + 1

y = −2x − 1

y = 2x + 1

y = 2x − 1

Question

What is the slope-intercept form equation of the line that passes through (1, 3) and (3, 7)?

 y = −2x + 1

 y = −2x − 1

 y = 2x + 1

 y = 2x − 1

mathmate · Answer

Assume an equation of the form y=ax+b.
Calculate the slope 
$$a=\frac{y_2-y_1}{x_2-x_1}$$

jenniferjuice · Answer

a = 4/2

jenniferjuice · Answer

what is b?

mathmate · Answer

That's good...  a=4/2=2.
Next, put (x1,y1) into the (x,y) of the assumed equation and solve for b

jenniferjuice · Answer

wait what

mathmate · Answer

We assumed the equation to be y=ax+b.

jenniferjuice · Answer

how to i find the equation of b?

mathmate · Answer

so put (1,3) into the equation, i.e. put x=1, y=3. Only b will be left as an unknown.  So solve for b.

jenniferjuice · Answer

b=3 ?

mathmate · Answer

(1,3) in y=2x+b  (a=2)
x=1, y=3, so
3=2(1)+b
what is b?

jenniferjuice · Answer

3-b=2 ?

jenniferjuice · Answer

b = 1 ?

mathmate · Answer

So what is b?
You need the value of b to find which choice to make!

jenniferjuice · Answer

b=-1

mathmate · Answer

3=2(1)+b
3=2+b
Subtract 2 from each side,
3-2=2-2+b
What would the value of b?

jenniferjuice · Answer

-1!

mathmate · Answer

The next line is
3-2=2-2+b
1=0+b
1=b