Question

Multiple Choice Which of the following is the \(x\) -intercept of the line \(y=2 x-5 ?\) \(\begin{array}{ll}{\text { (A) } x=-5} & {\text { (B) } x=5 \quad \text { (C) } x=0} \\ {\text { (D) } x=5 / 2} & {(\text { E) } x=-5 / 2}\end{array}\)

Short answer

The x-intercept of the given line y=2x-5 is x=5/2 or 2.5, so the correct option is (D) x=5/2.

Step-by-step solution

Understand line equation

The given line equation is y=2x-5. It is known as slope-intercept form of linear equation where 2 is the slope and -5 is the y-intercept.

Substituting y=0

The x-intercept is the x-coordinate where the line crosses the x-axis which is also the value of x when y equals to zero. Therefore, we substitute y=0 in the given equation to find the x-intercept. So, 0 = 2x - 5.

Solving for x

Now, solving the above equation for x would give us the x-intercept. Thus, adding 5 to both sides will give 2x = 5. Finally, dividing both sides by 2, we find that x = 5/2 or 2.5.