Graphing Linear Equations Unit Test

Question

14 of 1814 of 18 Items

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,
).

Answer 1

To find the slope and the y-intercept of the line that connects the two points A(0, 6) and B(-2, 2), we can follow these steps:

1. Calculate the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] where \( (x_1, y_1) \) are the coordinates of Point A (0, 6) and \( (x_2, y_2) \) are the coordinates of Point B (-2, 2).

   Substituting in the values: \[ m = \frac{2 - 6}{-2 - 0} = \frac{-4}{-2} = 2 \] The slope is \( 2 \).

2. Calculate the y-intercept (b). Since the y-intercept is where the line crosses the y-axis, we can use the y-coordinate of Point A, which is (0, 6). This means that the y-intercept is \( 6 \).

Thus, the final answer is: The slope is \( 2 \). The y-intercept is (0, 6).