Question

Please help me!!! In the xy-coordinate plane, the line segment connecting points A and B has a slope of 2. The x-coordinate of point B is 3 greater than x-coordinate of point A. How much greater is the y-coordinate of point B than the y-coordinate of pointe A?

Answer 1

ab= 2
point b=3 in total y=x +b so we have two answers already y=3+2 so what is that?

Answer 2

5 but remember how ab were that means multiply so your answer should be 6

Answer 3

Another way to look at it is using the slope formula and setting it equal to 2 (since the slope is 2)
\[\frac{ y_{2}-y_{1} }{ x_{2}-x_{1} } = 2\] So we're given that the x coordinate of point B (x2) is 3 more than the x-coordinate of A (x1). This is equivalent to saying that x2 = 3 + x1. Using that, I can substitute x2 in our formula for 3 + x1, giving us:
\[\frac{ y_{2}-y_{1} }{ 3+x_{1}-x_{1} } = \frac{ y_{2}-y_{1} }{ 3 }=2 \implies y_{2} - y_{1} = 6\]
At the very end, I multiplied both sides by 3 to get the y2 - y1 = 6. Well, we wanted to know how much larger the 2nd y-coordinate was than the first. Well, that's exactly what we have. The difference in their size is the difference in their values (subtracting the 2). So we see that y2 must be 6 larger than y1