find the equation of the line through (2,3) and (4,7)

Question

anonymous · Answer

Use the slope equation:
$$m=\frac{y_1-y_2}{x_1-x_2}$$
$$m=\frac{7-3}{4-2}$$
$$m=\frac{4}{2}=2$$
Then plug it into the equation:
$$y=mx+b$$
You can use any of the point to substitute y and x.
$$7=2(4)+b$$
$$7-8=b=-1$$
Therefore:
$$y=2x-1$$

anonymous · Answer

how did you get 2x
and can you explain "m=4/2=2 how did you get that =2

anonymous · Answer

@finaiized is correct!

precal · Answer

you can plot those two points and see that the equation does go through those 2 points

anonymous · Answer

The slope equation is $$y=mx+b$$
I first substituted in an x and y from the points you gave me to find b. Once I found b to be -1, I generalized the equation by replacing the numbers I substituted with y and x. If you plug in any point in y and x, then you'll get a point on the line.

As for the m=4/2, I subtracted points from each pair of points (Y1 from example, is the y coordinate of one of the points. Then I just subtracted Y1-Y2, and X1-X2, and got 4/2 which is the same as 2.

precal · Answer

I agree with finaiized

anonymous · Answer

make sense, thanks so much...i understand