Question
Using the graph, derive the equation of the line (1,-1) (0,-4) in slope-intercept form. (1 point) Responses y=3x−4 y equals 3 x minus 4 3x−y=4 3 x minus y equals 4 y=−3x−4 y equals negative 3 x minus 4 y=3x+4
Answers
Answered by
GPT-4o mini
To derive the equation of the line that passes through the points (1, -1) and (0, -4), we first need to calculate the slope of the line using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Let’s assign the coordinates from the two points:
- Point 1 (x_1, y_1) = (1, -1)
- Point 2 (x_2, y_2) = (0, -4)
Substituting the values:
\[
m = \frac{-4 - (-1)}{0 - 1} = \frac{-4 + 1}{-1} = \frac{-3}{-1} = 3
\]
The slope \( m \) is 3.
Next, we use the slope-intercept form of the equation of a line, which is:
\[
y = mx + b
\]
To find \( b \), the y-intercept, we can use one of the points. Let's use point (0, -4):
\[
-4 = 3(0) + b \implies b = -4
\]
Now we can write the equation using the slope and the y-intercept:
\[
y = 3x - 4
\]
So the equation of the line in slope-intercept form is:
\[
\textbf{y = 3x - 4}
\]
This corresponds to the response option: **y=3x−4**.
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Let’s assign the coordinates from the two points:
- Point 1 (x_1, y_1) = (1, -1)
- Point 2 (x_2, y_2) = (0, -4)
Substituting the values:
\[
m = \frac{-4 - (-1)}{0 - 1} = \frac{-4 + 1}{-1} = \frac{-3}{-1} = 3
\]
The slope \( m \) is 3.
Next, we use the slope-intercept form of the equation of a line, which is:
\[
y = mx + b
\]
To find \( b \), the y-intercept, we can use one of the points. Let's use point (0, -4):
\[
-4 = 3(0) + b \implies b = -4
\]
Now we can write the equation using the slope and the y-intercept:
\[
y = 3x - 4
\]
So the equation of the line in slope-intercept form is:
\[
\textbf{y = 3x - 4}
\]
This corresponds to the response option: **y=3x−4**.
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