Question

Graphing Linear Equations Unit Test
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Question
Use the image to answer the question.

An illustration shows a coordinate plane with four quadrants. The x and y axes extend from negative 10 to 10 in increments of 1. Two points are plotted on the graph. An upward slanting line connects the two points. Point A is plotted at coordinates left parenthesis 0 comma 6 right parenthesis. Point B is plotted at left parenthesis negative 2 comma 2 right parenthesis.

Identify the slope and y-intercept of the line. Provide the most simplified form of the slope.

(1 point)
The slope is
. The y-intercept is (0,
).
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Answer 1

To determine the slope and the y-intercept of the line connecting the points \( A(0, 6) \) and \( B(-2, 2) \), we'll use the following formulas:

### Step 1: Calculate the Slope
The slope \( m \) of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is calculated using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the coordinates of points \( A(0, 6) \) and \( B(-2, 2) \):
- \( (x_1, y_1) = (0, 6) \)
- \( (x_2, y_2) = (-2, 2) \)

Plugging in the values, we get:

\[
m = \frac{2 - 6}{-2 - 0} = \frac{-4}{-2} = 2
\]

### Step 2: Identify the Y-Intercept
The y-intercept of a line in the format \( y = mx + b \) is the value of \( b \) when \( x = 0 \). From the point, we know:

- Point \( A(0, 6) \) tells us that when \( x = 0 \), \( y = 6 \).

Thus, the y-intercept is \( (0, 6) \).

### Final Answers
- The slope is \( 2 \).
- The y-intercept is \( (0, 6) \).

So you can fill in the blanks as follows:

The slope is \( 2 \). The y-intercept is \( (0, 6) \).