Question

1. (04.05 mc) determine if the ordered pair (6, 4) is a solution to the inequality ( y < \frac{3}{4}x - 3 ). (1 point)

• no, because (6, 4) is above the line
• yes, because (6, 4) is below the line
• yes, because (6, 4) is on the line
• no, because (6, 4) is on the line

Explanation:

Step1: Substitute x=6 into the line equation

The line equation is \( y = \frac{3}{4}x - 3 \). Substitute \( x = 6 \):
\( y = \frac{3}{4}(6) - 3 = \frac{18}{4} - 3 = 4.5 - 3 = 1.5 \).

Step2: Compare y-value of (6,4) with the line's y-value

For the ordered pair \( (6, 4) \), the \( y \)-value is \( 4 \). The line at \( x = 6 \) has \( y = 1.5 \). Since \( 4 > 1.5 \), the point \( (6, 4) \) is above the line. The inequality is \( y < \frac{3}{4}x - 3 \), so \( 4 < 1.5 \) is false. Thus, \( (6, 4) \) is not a solution.

Answer:

No, because (6, 4) is above the line (the first option: "No, because (6,4) is above the line")