Question

part a
what are the x - and y-intercepts of the graph of 9x - 7y = -63?
x-intercept: (\square, \square)
y-intercept: (\square, \square)
part b
what is the graph of the equation 9x - 7y = -63?
\bigcirc a
graph a
\bigcirc b
graph b

Explanation:

Step1: Find x-intercept

To find the x-intercept, set \( y = 0 \) in the equation \( 9x - 7y = -63 \).
Substitute \( y = 0 \): \( 9x - 7(0) = -63 \)
Simplify: \( 9x = -63 \)
Solve for \( x \): \( x = \frac{-63}{9} = -7 \)
So, x-intercept is \( (-7, 0) \).

Step2: Find y-intercept

To find the y-intercept, set \( x = 0 \) in the equation \( 9x - 7y = -63 \).
Substitute \( x = 0 \): \( 9(0) - 7y = -63 \)
Simplify: \( -7y = -63 \)
Solve for \( y \): \( y = \frac{-63}{-7} = 9 \)
So, y-intercept is \( (0, 9) \).

Step3: Analyze the graphs for Part B

For the equation \( 9x - 7y = -63 \), we can rewrite it in slope - intercept form (\( y=mx + b \)):
\( -7y=-9x - 63 \)
\( y=\frac{9}{7}x + 9 \)
The y - intercept is \( (0,9) \) and the slope is positive (\( \frac{9}{7}>0 \)).
Looking at the two graphs:

• Graph A: The line has a negative slope (going down from left to right) and y - intercept at \( (0,9) \)? Wait, no, let's re - check. Wait, when we found the x - intercept is \( (-7,0) \) and y - intercept is \( (0,9) \). Let's check the direction of the line. The slope is \( \frac{9}{7}>0 \), so the line should be increasing (going up from left to right).
• Graph B: Let's see the intercepts. The y - intercept is \( (0,9) \) and as x increases, y increases (positive slope). Also, when x=-7, y = 0 (since x - intercept is (-7,0)). Let's check the position of the line. If we plot (-7,0) and (0,9), the line connecting these two points should have a positive slope. Graph B seems to have a positive slope and passes through (0,9) and when we move 7 units to the left from x = 0 (to x=-7), y should be 0. Graph B appears to match the intercepts and the slope.

Answer:

Part A

x - intercept: \( (-7, 0) \)
y - intercept: \( (0, 9) \)

Part B

The correct graph is Graph B (assuming Graph B is the one with positive slope passing through (0,9) and (-7,0))