Question

What is the y coordinate of the y−intercept of the line that passes through the points
(−4, −1) and (4, 5)?

Answer 1

Numerical Answers Expected!

Answer 2

Do you know the slope equation?
\[y = mx + b\]

Do you know how to find slope of the line on which two points are?
\[(y_2 - y_1) \div (x_2 - x_1)\]

Answer 3

i think

Answer 4

Slope formula is "rise over run" or difference in y divided by difference in x.
\[m = (y_2 −y_1 )÷(x_2 −x_1 )\]

Answer 5

I bring this up because the equation of a line's formula's "b" is the y-intercept you're looking for. Algebra can manipulate the line's formula to be:
\[y-mx=b\]
but you need to have
"m" the slope
and
x, y from a point (any point ON THE LINE will do)

Answer 6

So, find values for y, m, and x, and you can calculat your "b"!

Answer 7

Hint: you know two points on the line - just pick one! And "m", slope, is found from the slope formula from earlier.

I believe "y = mx + b" is called point-slope formula, on account of it's really a slope, a point, and a y-intercept (the y-value where your line hits the y-axis).

Answer 8

Umm, I think it's y=3/4x for like the slope or something..

Answer 9

or it's y=3/4x for the y intercept.

Answer 10

Yep,
\[y = \frac{ 3 }{ 4 }x + b\]
because "m" = 3/4. It's\[\frac{5 - (-1)}{4 - (-4)} = \frac{5 + (1)}{4 + (4)} = \frac{6}{8} = \frac{3}{4}\]

Answer 11

So, if you're looking for the y coordinates wouldn't it be like -1, 0, 1, 2, 3, 4, and 5?

Answer 12

The y coordinates could be anything for a line. If you think of any random real number for y, you could find a point with that y.
The y-intercept is special, since there can only be one y-intercept for a line. And it might not be a whole number.
Using the formula above, you solve for the y-intercept, "b", and take out the guesswork! :)

Answer 13

\[y-\frac{3}{4}x = b\]

Answer 14

Therefore you can find "b" if you know the x and y of one point. (Not just any x and y - it has to be the x and y of a point on the line!)

Answer 15

Choose (4, 5), for example. It's x = 4 and y = 5.\[y - \frac{3}{4}x = (5) - \frac{3}{4}(4) = 5- 3 = 2 = b\]

Answer 16

b = 2.

Answer 17

I did forget to mention what \[y_2, y_1, x_2, x_1\] were.

When looking at a point, it has an x and y. We are looking at one point, and another. So to differentiate between the two x's and two y's, we give each point a number, and label it's x and y with that point's number.
It's just labeling, and you can pick either point to be point 2, and the other will be point 1. Or you could pick point 1 first! Whatever you want.