Question

Which of the following lines does not intersect y = – 3x + 7?
A. y = – 3x – 7
B. y = 3x + 7
C. y = 3x – 7
D. y = 3x

Answer 1

The line y = - 3x - 7 does not intersect y = - 3x + 7

Given :

The equation of the line y = - 3x + 7

To find :

The lines does not intersect y = - 3x + 7

A. y = - 3x - 7

B. y = 3x + 7

C. y = 3x - 7

D. y = 3x

Solution :

Step 1 of 2 :

Write down the given equation of the line

Here the given given equation of the line is

y = - 3x + 7 - - - - - (1)

Which is of the form y = mx + c

Slope of the line = m = - 3

y - intercept of the line = c = 7

Step 2 of 2 :

Choose the correct option

We know that two given lines are said to be parallel to each other if they have the same slope

Also two given lines do not intersect if they are parallel to each other

Check for option A.

The equation of the line is

y = - 3x - 7 - - - - - (2)

Which is of the form y = mx + c

Slope of the line = m = - 3

y - intercept of the line = c = - 7

Thus we see that , slope of the line given by Equation 1 and Equation 2 are same

So the lines are parallel to each other

Thus the line y = - 3x - 7 does not intersect y = - 3x + 7

Hence the option A. y = - 3x - 7 is correct

Check for option B.

The equation of the line is

y = 3x + 7 - - - - - (3)

Which is of the form y = mx + c

Slope of the line = m = 3

y - intercept of the line = c = 7

Thus we see that , slope of the line given by Equation 1 and Equation 3 are not same

So the lines are not parallel to each other

Thus the line y = 3x + 7 intersects y = - 3x + 7

Hence the option B. y = 3x + 7 is not correct

Check for option C.

The equation of the line is

y = 3x - 7 - - - - - (4)

Which is of the form y = mx + c

Slope of the line = m = 3

y - intercept of the line = c = - 7

Thus we see that , slope of the line given by Equation 1 and Equation 4 are not same

So the lines are not parallel to each other

Thus the line y = 3x - 7 intersects y = - 3x + 7

Hence the option C. y = 3x - 7 is not correct

Check for option D.

The equation of the line is

y = 3x - - - - - (5)

Which is of the form y = mx + c

Slope of the line = m = 3

y - intercept of the line = c = 0

Thus we see that , slope of the line given by Equation 1 and Equation 5 are not same

So the lines are not parallel to each other

Thus the line y = 3x intersects y = - 3x + 7

Hence the option D. y = 3x is not correct

Final answer : The correct option is A. y = - 3x - 7

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