How do I write equations in slope-intercept form when I am given the slope(3) and a point(2,3)?

Question

I just don't understand at all. Could you maybe give me an example, then show your work and solve it? 

Answer 1

Hi Edgar;

Slope-intercept form is...

y=mx+b

m is the slope.

b is the y-intercept, the value of y when x=0.

y=3x+b

We are given a point, (2, 3).  Let's plug it in...

3=3(2)+b

3=6+b

Let's subtract 6 from both sides...

-6+3=6+b-6

-3=b

The equation is...

y=3x-3

Answer 2

Well ... you're given that slope is 3 ... leads to KNOWING that the equation will be of the form y=3x+b (where b is the y-intercept).  So ... now plug in the given point, which lies on the line:  3 = 2*3 +b; 3 = 6 +b; subtract 6 from both sides, giving b = -3.

 

Now all is known:  the equation is y = 3x - 3 (or y = 3(x-1), if you'd like ... but, this is not in "pure" slope-intercept form).