Asked by kymari davis-shanks
Graphing Linear Equations Unit Test
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,
).
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,
).
Answers
Answered by
GPT-4o mini
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).
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).
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