Answer:
Explanation:
Hey Sam, this seems like "simple" algebra, but it's a lot of implied understanding. everyone asks about this kind of question. it's really amazing how teacher can't seem to teach this type of problem. It's not the students, but the teachers that fail at teaching this . anyway...
we are given two points and asked to write an equation for the line passing through the two points.
So, first, do you understand the idea of "an equation of a line" ?
we could use the slope-intercept formula y=mx+b as the template for what we want to make. But you also have to understand what that formula is explaining. The idea or concept is important b/c so much more math is built on this. The equation of a line.
just remember the two formula's slope-intercept and point-slope, they are very related. Y=mx+b and Y-y1=m(x-x1) respectively.
the given points:
point P1 (2,7) in the form (x1,y1)
point P2(0,-5) in the form (x2,y2)
step one:
slope = m
m = (y2-y1) / (x2-x1)
now plug in the given points , to find the slope.
m = (-5-7) / (0-2)
m = -12 / -2
m = 12 / 2
m = 6
Step two:
since we've found the slope, now use the point-slope formula with either of the given points and then solve for Y, that is, isolate Y. This will automatically give us the slope-intercept form and the equation for the line :) I'll use P1
Y - y1 = m(x -x1)
Y - 7 = 6(x-2)
I just plugged in the point P1 for x1,y1 and m=6, now use your algebra skillz
Y - 7 = 6x -12
Y = 6x -12 +7
Y = 6x - 5
there is your answer, and the equation for the line in slope-intercept form. :)