Question

which shows -1.75 graphed on the number line?
(number lines as shown in the image: first with dot near 2, second with dot between -2 and -1, third with dot near 1, fourth with dot between -2 and -1)

Explanation:

Step1: Understand -1.75's position

-1.75 is between -2 and -1 (since -2 < -1.75 < -1). It's 0.75 away from -2 (or 0.25 away from -1, as \(|-1.75 - (-2)| = 0.25\)? Wait, no: \( -2 + 0.25 = -1.75\)? Wait, no: \( -2 + 0.25 = -1.75\)? Wait, -2 to -1 is 1 unit. 0.75 of the way from -2 to -1? Wait, -1.75 = -2 + 0.25? Wait, no: -2 + 0.25 is -1.75? Wait, -2 + 0.25 = -1.75? Yes, because -2 + 0.25 = -1.75. So it's 0.25 units to the right of -2, or 0.75 units to the left of -1.

Step2: Analyze each number line

• First graph: dot near 2 (positive, wrong).
• Second graph: dot at -2 (but -1.75 is not -2, it's between -2 and -1, so wrong).
• Third graph: dot near 1 (positive, wrong).
• Fourth graph: dot between -2 and -1, closer to -2? Wait, -1.75 is 0.25 above -2 (since -2 + 0.25 = -1.75) and 0.75 below -1 (since -1 - 0.75 = -1.75). So the dot should be 1/4 of the way from -2 to -1 (since 0.25 is 1/4 of 1 unit). Looking at the fourth number line, the dot is between -2 and -1, which matches -1.75's position (between -2 and -1). The other graphs: first is positive, second is at -2, third is positive. So the fourth graph (the bottom one) has the dot between -2 and -1, which is where -1.75 should be.

Answer:

The bottom number line (the fourth one, with the dot between -2 and -1)