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Line m contains the points (4, 16) and (0, 8). At what point will line m intersect with line n if the equation of line n is -8x+4y=24 ?

A) (0, 0)
B) (-4, 0)
C) The lines don't intersect
D) The lines intersect at an infinite number of points

Respuesta :

The correct option regarding the point at which the linear functions intersect is given by:

C) The lines don't intersect.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

For line m, we have that the y-intercept is of b = 8. When x changes by 4, y changes by 8, hence the slope is of 2, and the equation is:

y = 2x + 8.

Line n, in slope-intercept format, is given by:

-8x + 4y = 24

4y = 8x + 24

y = 2x + 6

Hence:

2x + 8 = 2x + 6

0x = -2

Which is impossible, hence they do not intersect and option C is correct.

More can be learned about linear functions at https://brainly.com/question/24808124

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