Which of the following statements must be true in order for the line represented by the equation y = mx + b to have a negative x

Question

2 years ago

5

Which of the following statements must be true in order for the line represented by the equation y = mx + b to have a negative x

-intercept?
The signs of the values of m and b are the same.

The value of m is positive while the value of b is negative.

The value of m is negative while the value of b is positive.

The signs of the values of m and b do not affect the sign of the x-intercept.

Mathematics

2 answers:

inn [45] · Answer 1 · 2023-06-15T07:39:57+03:00

inn [45]2 years ago

6 0

First option: <span>The signs of the values of m and b are the same.</span>

kumpel [21] · Answer 2 · 2023-06-15T10:00:12+03:00

Answer:

Option A is correct

The signs of the values of m and b are the same.

Step-by-step explanation:

x-intercept states that the graph crosses the x-axis.

Substitute y =0 and solve for x:

As per the statement:

Given the equation:

$y=mx+b$

where, m is the slope and b is the y-intercept.

It is also given: A negative x-intercept

⇒negative x-intercept = (-x, 0)

substitute in [1] we have;

$0 = -mx+b$

Add mx to both sides we have;

$mx = b$

or

b = mx

Since, the sign of m and b are same.

Therefore, the following statements must be true in order for the line represented by the equation y = mx + b to have a negative x-intercept is, The signs of the values of m and b are the same.