Question

y + 7 = -(x - 1)
graph of line b:
graph of a line on a coordinate plane
answer attempt 1 out of 2
the x-intercept of line a is blank and the x-intercept of line b is blank.

Explanation:

Step1: Find x-intercept of Line A (equation \( y + 7 = -(x - 1) \))

To find the x-intercept, set \( y = 0 \) in the equation.
\( 0 + 7 = -(x - 1) \)
\( 7 = -x + 1 \)
Subtract 1 from both sides: \( 7 - 1 = -x \)
\( 6 = -x \)
Multiply both sides by -1: \( x = -6 \)? Wait, no, wait. Wait, let's recheck. Wait, \( y + 7 = -(x - 1) \), when \( y = 0 \):
\( 0 + 7 = -x + 1 \)
\( 7 - 1 = -x \)
\( 6 = -x \) → \( x = -6 \)? Wait, but maybe I made a mistake. Wait, no, let's do it again.
\( y + 7 = - (x - 1) \)
Set \( y = 0 \):
\( 0 + 7 = -x + 1 \)
\( 7 = -x + 1 \)
Subtract 1: \( 6 = -x \) → \( x = -6 \)? Wait, but the graph of Line B: let's check Line B's x-intercept.

Step2: Find x-intercept of Line B (from the graph)

The graph of Line B crosses the x-axis at \( x = -8 \) (since the line intersects the x-axis at (-8, 0)). Wait, but let's confirm Line A's equation. Wait, the equation given is \( y + 7 = -(x - 1) \), which is Line A? Wait, the problem says "Line A" has equation \( y + 7 = -(x - 1) \) and Line B is the graph. Wait, maybe I mixed up. Wait, the equation is for Line A, and the graph is Line B.

So for Line A (equation \( y + 7 = -(x - 1) \)):
x-intercept: set \( y = 0 \):
\( 0 + 7 = -x + 1 \)
\( 7 - 1 = -x \)
\( 6 = -x \) → \( x = -6 \)? Wait, no, that can't be. Wait, maybe the equation is \( y + 7 = - (x - 1) \), so \( y = -x + 1 - 7 = -x - 6 \). So when \( y = 0 \), \( 0 = -x - 6 \) → \( x = -6 \). But the graph of Line B: looking at the graph, the line crosses the x-axis at (-8, 0), so x-intercept is -8. Wait, but the problem says "The x-intercept of Line A is [ ] and the x-intercept of Line B is [ ]".

Wait, maybe I misread the equation. Wait, the equation is \( y + 7 = - (x - 1) \), so let's expand it: \( y + 7 = -x + 1 \), so \( y = -x + 1 - 7 = -x - 6 \). So x-intercept when \( y = 0 \): \( 0 = -x - 6 \) → \( x = -6 \). But the graph of Line B: the line in the graph crosses the x-axis at x = -8 (since it goes through (-8, 0)). So Line A's x-intercept is -6, Line B's is -8? Wait, but maybe the equation is for Line B? No, the text says "Graph of Line B" and the equation is above, maybe Line A is the equation and Line B is the graph.

Wait, let's re-express:

For Line A (equation \( y + 7 = - (x - 1) \)):
To find x-intercept, set \( y = 0 \):
\( 0 + 7 = - (x - 1) \)
\( 7 = -x + 1 \)
\( -x = 7 - 1 = 6 \)
\( x = -6 \)

For Line B (graph):
The line intersects the x-axis at (-8, 0), so x-intercept is -8.

Answer:

The \( x \)-intercept of Line A is \(-6\) and the \( x \)-intercept of Line B is \(-8\).