Question

How do I solve this?
1. A line passes through A(3,7) and B(-4,9). Find the value of a if C(a,1) is on the line.

Answer 1

can you find the slope of line AB ?

Answer 2

have the formula for slope or should i give it ?

Answer 3

The slope of the line through points (x1,y1) and (x2,y2) is given by :
\(\huge m=\frac{y_1-y_2}{x_1-x_2}\)
now,just put the values and find m.

Answer 4

to continue, one option: choose one of your given points (x, y) and with the m you just calculated, put in the equation of the line and find b
y = mx + b

now, for any point on the line you have the general equation of the line. for the point (a, 1) y = 1 substitute in the eqn and solve for a

another option is to use the formula for the slope and the points for A and C or the points for B and C to find a. The slope of a line is the same between any two points on that line.

Answer 5

hey @triciaal can you exlpain more, i am really lost

Answer 6

did you find the slope?

Answer 7

are you there?

Answer 8

I can't help you if you are not responding?

Answer 9

One way to do things in math is to say you already have the answer. And that's what I'm going to do here. The answer is y=mx+b. Not just any y=mx+b, but this is in fact our exact line that goes through our points. We have the answer. Ok, but telling someone the slope is m or the y-intercept is b isn't something most people will appreciate much.

That's fine, so what do we know about our line y=mx+b? Well it goes through (3,7) and (-4,9) so that means if we plug in 3 for x in our equation y=mx+b then our y must be 7, right? That's what (3,7) falling on our line means. Pretty straightforward right? So let's plug it in just like that:

7=m3+b

Let's also do that with the other point

9=m(-4)+b

Alright cool. Now you have two equations and two unknowns. That means we can solve for one and plug it into the other to solve so we can uncover our hidden slope and y-intercept. Try it out, good luck.