Question

uestion 13 (4 points)

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What is the y-intercept of the line passing through the points
(2,5) and (-2,-11)
Question 13 options:

4


-3


3


-4

Answer 1

To find the y-intercept of the line passing through the points (2, 5) and (-2, -11), we first need to determine the equation of the line in slope-intercept form (y = mx + b).

1. **Calculate the slope (m)**:
The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (2, 5) and (-2, -11):
\[
m = \frac{-11 - 5}{-2 - 2} = \frac{-16}{-4} = 4
\]

2. **Use the point-slope form to find the line's equation**:
We can use one of the points and the slope to find the equation. Using point (2, 5):
\[
y - 5 = 4(x - 2)
\]
Expanding this:
\[
y - 5 = 4x - 8
\]
\[
y = 4x - 3
\]

Now, we can read the y-intercept (b) directly from the equation \(y = 4x - 3\), which is \(-3\).

So, the y-intercept of the line is \(-3\).

**Answer: -3**