Question

A coordinate plane with a line passing through (negative 4, 3), (0, 1), and (2, 0).
What are the slope and y-intercept of the linear function graphed to the left?

slope: –2; y-intercept: 2
slope: ; y-intercept: 1
slope: ; y-intercept: 2
slope: 2; y-intercept: 1

Answer 1

To determine the slope and y-intercept of the line passing through the points \((-4, 3)\), \((0, 1)\), and \((2, 0)\), we can use the coordinates provided.

1. **Calculating the Slope (m)**:
The slope \(m\) can be calculated using any two points on the line with the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's use the points \((0, 1)\) and \((2, 0)\):
\[
m = \frac{0 - 1}{2 - 0} = \frac{-1}{2} = -\frac{1}{2}
\]

We can also check the slope using the points \((-4, 3)\) and \((0, 1)\):
\[
m = \frac{1 - 3}{0 - (-4)} = \frac{-2}{4} = -\frac{1}{2}
\]

The slope should remain consistent across any two points that lie on the line, confirming our slope.

2. **Finding the y-intercept (b)**:
The y-intercept can be determined directly from the point where \(x = 0\). From the point \((0, 1)\), we see that the y-intercept \(b\) is 1.

Now we can summarize the results:

- Slope: \( -\frac{1}{2} \)
- Y-intercept: \( 1 \)

From the given options, none seem to have a matching slope of \(-\frac{1}{2}\). The calculations show that there's a potential mismatch in options provided.

If we take previously evaluated options:

- \(slope: -2; y-intercept: 2 (Not matching)\)
- \(slope: ; y-intercept: 1 (Not complete)\)
- \(slope: ; y-intercept: 2 (Not complete)\)
- \(slope: 2; y-intercept: 1 (Not matching)\)

It appears none of those matches adequately reflect the calculated slope of \(-\frac{1}{2}\) and y-intercept of \(1\). If there is any opportunity to revisit the data or points to confirm the slope calculation, it could clarify the mismatch in expected answers.