Question
What is the equation of this line in slope-intercept form?
Responses
y=3x−2
y equals 3 x minus 2
y=−13x+2
y equals negative 1 third x plus 2
y=−3x+2
y equals negative 3 x plus 2
y = 3x + 2
y = 3 x + 2
Number graph ranging from negative 5 to 5 on the x and y axes. A line is drawn on the graph that passes through the labeled points begin ordered pair negative 1 comma 5 end ordered pair and begin ordered pair 1 comma negative 1 end ordered pair
Responses
y=3x−2
y equals 3 x minus 2
y=−13x+2
y equals negative 1 third x plus 2
y=−3x+2
y equals negative 3 x plus 2
y = 3x + 2
y = 3 x + 2
Number graph ranging from negative 5 to 5 on the x and y axes. A line is drawn on the graph that passes through the labeled points begin ordered pair negative 1 comma 5 end ordered pair and begin ordered pair 1 comma negative 1 end ordered pair
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the equation of the line that passes through the points (-1, 5) and (1, -1), we can follow these steps:
1. **Calculate the slope (m)** of the line using the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (-1, 5) and (1, -1):
\[
m = \frac{-1 - 5}{1 - (-1)} = \frac{-6}{2} = -3
\]
2. **Use the point-slope form** of a line to find the equation. The point-slope form is:
\[
y - y_1 = m(x - x_1)
\]
We can use one of the points, such as (-1, 5):
\[
y - 5 = -3(x - (-1))
\]
\[
y - 5 = -3(x + 1)
\]
3. **Distribute and simplify** the equation:
\[
y - 5 = -3x - 3
\]
\[
y = -3x + 2
\]
Now the equation is in slope-intercept form, which is \(y = mx + b\). Thus, the line's equation is:
**y = -3x + 2**
So the correct response from your options is:
- \(y = -3x + 2\)
- \(y\) equals negative \(3\) times \(x\) plus \(2\).
1. **Calculate the slope (m)** of the line using the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (-1, 5) and (1, -1):
\[
m = \frac{-1 - 5}{1 - (-1)} = \frac{-6}{2} = -3
\]
2. **Use the point-slope form** of a line to find the equation. The point-slope form is:
\[
y - y_1 = m(x - x_1)
\]
We can use one of the points, such as (-1, 5):
\[
y - 5 = -3(x - (-1))
\]
\[
y - 5 = -3(x + 1)
\]
3. **Distribute and simplify** the equation:
\[
y - 5 = -3x - 3
\]
\[
y = -3x + 2
\]
Now the equation is in slope-intercept form, which is \(y = mx + b\). Thus, the line's equation is:
**y = -3x + 2**
So the correct response from your options is:
- \(y = -3x + 2\)
- \(y\) equals negative \(3\) times \(x\) plus \(2\).
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