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Are the graphs of the given equations identical lines parallel lines are lines intersecting on a single point

Are the graphs of the given equations identical lines parallel lines are lines intersecting-example-1

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6 votes
They are intersecting lines
User Maddesa
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8.1k points
10 votes

The graphs of the equations 7x+y = 7 and x+6y = -48 intersect at a single point and the correct option is C.

To determine without graphing whether the graphs of the two given equations are identical lines, parallel lines, or lines intersecting at a single point, we can use the following steps:

1. Solve both equations for y.

Equation 1:

7x + y = 7

y = -7x + 7

Equation 2:

x + 6y = -48

6y = -x - 48

y = -1/6x - 8

2. Compare the slopes and y-intercepts of the two equations.

Equation 1: Slope = -7, y-intercept = 7

Equation 2: Slope = -1/6, y-intercept = -8

Since the slopes are different, the two lines are not identical nor parallel. Therefore, the graphs of the two lines must intersect at a single point and the correct option is C.

User Yiran
by
8.4k points

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