Question

A table of values representing a linear relationship is shown.
x y
-2 -7
0 -3
2 1
4 5
Which equation models this relationship in slope-intercept form?
y = 2x - 3
y = -2x - 3
y = 1/2x - 3
y = -4x - 3

Answer 1

To find the equation that models the linear relationship in slope-intercept form \(y = mx + b\), we first need to calculate the slope (\(m\)) using two points from the table.

Let's use the points \((-2, -7)\) and \((2, 1)\):

The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the points:
\[
m = \frac{1 - (-7)}{2 - (-2)} = \frac{1 + 7}{2 + 2} = \frac{8}{4} = 2
\]

Now that we have the slope \(m = 2\), we can use one of the points to find the y-intercept \(b\). Let's use the point \((0, -3)\) because it already has the \(y\) value for \(x = 0\), implying that \(b = -3\).

Thus, the equation of the line in slope-intercept form is:
\[
y = 2x - 3
\]

Now let's verify that this equation holds true for the other points in the table.

1. For \(x = -2\):
\[
y = 2(-2) - 3 = -4 - 3 = -7 \quad \text{(Point is correct)}
\]

2. For \(x = 2\):
\[
y = 2(2) - 3 = 4 - 3 = 1 \quad \text{(Point is correct)}
\]

3. For \(x = 4\):
\[
y = 2(4) - 3 = 8 - 3 = 5 \quad \text{(Point is correct)}
\]

Since the equation holds for all points, the correct equation that models this relationship in slope-intercept form is:
\[
\boxed{y = 2x - 3}
\]