Given the point-slope equation Y - 5 = -2(X + 3), what is the y-intercept of the line?

Given the point-slope equation Y - 5 = -2(X + 3), what is the y-intercept of the line?

• A. 5
• B. -1
• C. 3
• D. 0

Answer: (B)

To find the y-intercept of the line represented by the point-slope equation \(Y - 5 = -2(X + 3)\), we first need to rearrange the equation into slope-intercept form, which is \(Y = mX + b\), where \(b\) is the y-intercept. Starting with the given equation: \[ Y - 5 = -2(X + 3) \] we first distribute \(-2\) on the right side: \[ Y - 5 = -2X - 6 \] Next, add \(5\) to both sides to isolate \(Y\): \[ Y = -2X - 6 + 5 \] \[ Y = -2X - 1 \] Now, in the slope-intercept form, we can clearly see that the term \(-1\) is the y-intercept, which tells us the point where the line crosses the y-axis. Thus, the correct y-intercept of the line is \(-1\).

To find the y-intercept of the line represented by the point-slope equation (Y - 5 = -2(X + 3)), we first need to rearrange the equation into slope-intercept form, which is (Y = mX + b), where (b) is the y-intercept.

Starting with the given equation:

[

Y - 5 = -2(X + 3)

]

we first distribute (-2) on the right side:

[

Y - 5 = -2X - 6

]

Next, add (5) to both sides to isolate (Y):

[

Y = -2X - 6 + 5

]

[

Y = -2X - 1

]

Now, in the slope-intercept form, we can clearly see that the term (-1) is the y-intercept, which tells us the point where the line crosses the y-axis.

Thus, the correct y-intercept of the line is (-1).