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Math  /  Algebra

Question6. What are the xx-and yy-intercepts of the graph of 9x−7y=−639 x-7 y=-63 ? Graph the equation. (2pts) xx-intercept: □\square yy-intercept:

Studdy Solution

STEP 1

1. The equation of the line is given in standard form: 9x−7y=−639x - 7y = -63.
2. The xx-intercept occurs where y=0y = 0.
3. The yy-intercept occurs where x=0x = 0.

STEP 2

1. Find the xx-intercept.
2. Find the yy-intercept.
3. Graph the equation using the intercepts.

STEP 3

To find the xx-intercept, set y=0y = 0 in the equation 9x−7y=−639x - 7y = -63.
9x−7(0)=−63 9x - 7(0) = -63
This simplifies to:
9x=−63 9x = -63

STEP 4

Solve for xx:
x=−639 x = \frac{-63}{9}
x=−7 x = -7
The xx-intercept is (−7,0)(-7, 0).

STEP 5

To find the yy-intercept, set x=0x = 0 in the equation 9x−7y=−639x - 7y = -63.
9(0)−7y=−63 9(0) - 7y = -63
This simplifies to:
−7y=−63 -7y = -63

STEP 6

Solve for yy:
y=−63−7 y = \frac{-63}{-7}
y=9 y = 9
The yy-intercept is (0,9)(0, 9).

STEP 7

To graph the equation, plot the intercepts (−7,0)(-7, 0) and (0,9)(0, 9) on a coordinate plane. Draw a straight line through these points to represent the equation 9x−7y=−639x - 7y = -63.
The xx-intercept is (−7,0)(-7, 0) and the yy-intercept is (0,9)(0, 9).

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