Question

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.

Answer 1

First option: The signs of the values of m and b are the same.

Answer 2

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.