Question

What is the x-coordinate of the x-intercept of the line that passes through points (-5, 3) and (1, -3)?

Answer 1

You want to find the point (x,0) (the point which intercepts the x axis). To do so, you must find the linear equation of the function which is going through these points, and then you plug y=0.
Can you manage ?

Answer 2

So how would I find the linear equation of the function then given the given information?

Answer 3

A linear equation is of this form: y=ax+b, right? The a is the slope, and the b the y-intercept.
So, if you have to couples \[(x_{1}, y_{1}) and (x_{2},y_{2})\], you get :
\[a=\frac{ y_{2}-y_{1} }{ x_{2}-x_{1} }\]

Afterward, you want to find the value of b, which is pretty easy.
You choose one of your couple, and you plug you values into your equation y=ax+b.
In your case, you'll get, example: -3=a(1)+b (your a has a value that you find earlier). So, you only have to isolate b in your equation and you win :)

Answer 4

So is my y value 4.5? or 3/2 in slope form? Now that I have that, how would I find the x?

Answer 5

first we find the slope using the slope formula :
slope(m) = (y2 - y1) / (x2 - x1)
(-5,3) x1 = -5 and y1 = 3
(1,-3) x2 = 1 and y2 = -3
now we sub
slope(m) = (-3 - 3) / (1 - (-5)
slope(m) = -6/6
slope(m) = -1

now we will use y = mx + b form and find b because we already know the other terms
you can use either of your set of points...
(-5,3) x = -5 and y = 3
slope(m) = -1
now we sub
y = mx + b
3 = -1(-5) + b
3 = 5 + b
3 - 5 = b
-2 = b
so our equation is : y = -x - 2
To find the x intercept, sub in 0 for y
y = -x - 2
0 = -x - 2
x = -2
your x coordinate of the x intercept (-2,0) is -2

Answer 6

Wow, it was a bad simple math mistake on my part when getting the slope, after that, thanks for the info and help! I got it now!

Answer 7

good to hear :)