Question

ixl.com/math/grade-8/checkpoint-slope-and-linear-equations
which statements are true? select all that apply.
the slope of \\(\overline{ab}\\) is equal to the slope of \\(\overline{bd}\\).

Explanation:

Step1: Find coordinates of points

First, identify the coordinates of points \( A \), \( B \), and \( D \). From the graph:

• Point \( B \) is at \( (0, 4) \)
• Point \( A \) is at \( (7, 7) \)
• Point \( D \) is at \( (7, 4) \)

Step2: Calculate slope of \( \overline{AB} \)

The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). For \( \overline{AB} \), using \( A(7, 7) \) and \( B(0, 4) \):
\( m_{AB} = \frac{7 - 4}{7 - 0} = \frac{3}{7} \)

Step3: Calculate slope of \( \overline{BD} \)

For \( \overline{BD} \), using \( B(0, 4) \) and \( D(7, 4) \):
\( m_{BD} = \frac{4 - 4}{7 - 0} = \frac{0}{7} = 0 \)

Step4: Compare slopes

\( m_{AB} = \frac{3}{7} \) and \( m_{BD} = 0 \). Since \( \frac{3}{7}
eq 0 \), the slopes are not equal. Wait, but maybe I misread the segments? Wait, maybe the segment is \( AC \) or another? Wait, no, the problem says "the slope of \( \overline{AB} \) is equal to the slope of \( \overline{BD} \)". Wait, no, maybe \( BD \) is horizontal, \( AB \) is a line with positive slope. Wait, maybe the user's question is to check if that statement is true? Wait, the initial statement: "The slope of \( \overline{AB} \) is equal to the slope of \( \overline{BD} \)". Let's recalculate.

Wait, maybe I made a mistake in coordinates. Wait, point \( D \): from \( B(0,4) \) to \( D(7,4) \), so horizontal line, slope 0. \( AB \): from \( B(0,4) \) to \( A(7,7) \), change in y is \( 7 - 4 = 3 \), change in x is \( 7 - 0 = 7 \), so slope \( 3/7 \). \( BD \) is horizontal, slope 0. So \( 3/7
eq 0 \), so the statement is false? Wait, but maybe the segment is \( AC \) or another? Wait, no, the problem's statement is about \( AB \) and \( BD \). Wait, maybe I misidentified the points. Wait, let's check again.

Wait, point \( B \) is (0,4), point A is (7,7), point D is (7,4). So \( BD \) is vertical? Wait no, \( B(0,4) \) to \( D(7,4) \): x changes from 0 to 7, y stays 4. So it's horizontal, slope 0. \( AB \): from (0,4) to (7,7), slope (7-4)/(7-0)=3/7. So they are not equal. But maybe the question is to check this statement. Wait, the user's problem is to determine if "The slope of \( \overline{AB} \) is equal to the slope of \( \overline{BD} \)" is true. So the answer would be that the statement is false. But maybe I made a mistake. Wait, maybe the segment is \( AD \)? No, the problem says \( BD \).

Wait, perhaps the original problem has a typo, or I misread the points. Wait, let's re-express:

Wait, \( \overline{BD} \): from \( B(0,4) \) to \( D(7,4) \): slope is 0. \( \overline{AB} \): from \( B(0,4) \) to \( A(7,7) \): slope 3/7. So they are not equal. So the statement "The slope of \( \overline{AB} \) is equal to the slope of \( \overline{BD} \)" is false.

But wait, maybe the segment is \( AC \) or another. Wait, no, the problem's statement is as given. So according to the calculations, the slopes are not equal.

Answer:

The statement "The slope of \( \overline{AB} \) is equal to the slope of \( \overline{BD} \)" is false because \( m_{AB} = \frac{3}{7} \) and \( m_{BD} = 0 \), and \( \frac{3}{7}
eq 0 \).