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

1 answer

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.