Question

4 matching 4 points
a $y = -\frac{1}{2}x - 4$ e. $y = \frac{3}{4}x + 1$
b. $y = -4x - 3$ f. $y = x - 1$
c. $y = \frac{3}{4}x - 4$ g. $y = -\frac{1}{2}x + 4$
d. $y = x - 5$ h. $y = -4x + 5$
a
d
b
c

Explanation:

To solve this matching problem, we analyze the slopes and y - intercepts of the linear equations (in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept) to find equivalent or related equations.

For equation A (\(y=-\frac{1}{2}x - 4\))

We look for an equation with the same slope (\(m =-\frac{1}{2}\)) and a different y - intercept or a related form. The equation \(G:y =-\frac{1}{2}x + 4\) has the same slope (\(m=-\frac{1}{2}\)) as equation A. So \(A\) matches with \(G\).

For equation D (\(y=x - 5\))

We look for an equation with the same slope (\(m = 1\)). The equation \(F:y=x - 1\) has the same slope (\(m = 1\)) as equation D. So \(D\) matches with \(F\).

For equation B (\(y=-4x - 3\))

We look for an equation with the same slope (\(m=-4\)). The equation \(H:y=-4x + 5\) has the same slope (\(m=-4\)) as equation B. So \(B\) matches with \(H\).

For equation C (\(y=\frac{3}{4}x - 4\))

We look for an equation with the same slope (\(m=\frac{3}{4}\)). The equation \(E:y=\frac{3}{4}x + 1\) has the same slope (\(m=\frac{3}{4}\)) as equation C. So \(C\) matches with \(E\).

Final Matches:

• \(A\) - \(G\)
• \(D\) - \(F\)
• \(B\) - \(H\)
• \(C\) - \(E\)

Answer:

To solve this matching problem, we analyze the slopes and y - intercepts of the linear equations (in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept) to find equivalent or related equations.

For equation A (\(y=-\frac{1}{2}x - 4\))

We look for an equation with the same slope (\(m =-\frac{1}{2}\)) and a different y - intercept or a related form. The equation \(G:y =-\frac{1}{2}x + 4\) has the same slope (\(m=-\frac{1}{2}\)) as equation A. So \(A\) matches with \(G\).

For equation D (\(y=x - 5\))

We look for an equation with the same slope (\(m = 1\)). The equation \(F:y=x - 1\) has the same slope (\(m = 1\)) as equation D. So \(D\) matches with \(F\).

For equation B (\(y=-4x - 3\))

We look for an equation with the same slope (\(m=-4\)). The equation \(H:y=-4x + 5\) has the same slope (\(m=-4\)) as equation B. So \(B\) matches with \(H\).

For equation C (\(y=\frac{3}{4}x - 4\))

We look for an equation with the same slope (\(m=\frac{3}{4}\)). The equation \(E:y=\frac{3}{4}x + 1\) has the same slope (\(m=\frac{3}{4}\)) as equation C. So \(C\) matches with \(E\).

Final Matches:

• \(A\) - \(G\)
• \(D\) - \(F\)
• \(B\) - \(H\)
• \(C\) - \(E\)