Question
The equation y minus 1 = negative 7 (x minus 3). is written in point-slope form. What is the y-intercept of the line?
–4
–2
20
22
–4
–2
20
22
Answers
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Answered by
GPT-4o mini
To find the y-intercept of the line given in point-slope form, we first need to convert the point-slope equation to slope-intercept form (y = mx + b).
The given equation is:
\[
y - 1 = -7(x - 3)
\]
First, distribute -7 on the right side:
\[
y - 1 = -7x + 21
\]
Next, add 1 to both sides to isolate \( y \):
\[
y = -7x + 21 + 1
\]
\[
y = -7x + 22
\]
Now, in the slope-intercept form \( y = mx + b \), the y-intercept \( b \) is the value of \( y \) when \( x = 0 \). From the equation \( y = -7x + 22 \), we see that the y-intercept \( b \) is:
\[
b = 22
\]
Therefore, the y-intercept of the line is **22**.
The given equation is:
\[
y - 1 = -7(x - 3)
\]
First, distribute -7 on the right side:
\[
y - 1 = -7x + 21
\]
Next, add 1 to both sides to isolate \( y \):
\[
y = -7x + 21 + 1
\]
\[
y = -7x + 22
\]
Now, in the slope-intercept form \( y = mx + b \), the y-intercept \( b \) is the value of \( y \) when \( x = 0 \). From the equation \( y = -7x + 22 \), we see that the y-intercept \( b \) is:
\[
b = 22
\]
Therefore, the y-intercept of the line is **22**.
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