To find the [tex]\(y\)[/tex]-intercept of the line passing through the given points, we need to follow these steps:
1. Identify two points to calculate the slope of the line.
2. Use the slope to find the [tex]\(y\)[/tex]-intercept.
### Step 1: Calculate the Slope (m)
The given points from the table are:
[tex]\[
(x_1, y_1) = (-56, 66)
\][/tex]
[tex]\[
(x_2, y_2) = (-42, 58)
\][/tex]
The formula for the slope (m) between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Plugging in the values:
[tex]\[
m = \frac{58 - 66}{-42 - (-56)} = \frac{58 - 66}{-42 + 56} = \frac{-8}{14} = -0.5714285714285714
\][/tex]
### Step 2: Find the [tex]\(y\)[/tex]-intercept (b)
The equation of a line in slope-intercept form is:
[tex]\[
y = mx + b
\][/tex]
To find the [tex]\(y\)[/tex]-intercept (b), we can use one of the points and the slope. Let's use the point [tex]\((-56, 66)\)[/tex]:
[tex]\[
66 = (-0.5714285714285714) \cdot (-56) + b
\][/tex]
First, calculate [tex]\((-0.5714285714285714) \cdot (-56)\)[/tex]:
[tex]\[
-0.5714285714285714 \cdot -56 = 32
\][/tex]
Now substitute back in:
[tex]\[
66 = 32 + b
\][/tex]
Solve for [tex]\(b\)[/tex]:
[tex]\[
b = 66 - 32 = 34
\][/tex]
Thus, the [tex]\(y\)[/tex]-intercept of the line is:
[tex]\[
b = 34
\][/tex]
