Which of the following statements about the graph of y equals three fourths x minus 1

Question

are​ true?
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Part 1
Select all that apply.
A.
The​ y-intercept is three fourths
.
B.
The line passes through the point left parenthesis 0 comma negative three fourths right parenthesis
.
C.
The slope of the line is three fourths
.
D.
The slope of the line is minus1.
E.
The line passes through the point left parenthesis 0 comma 1 right parenthesis.
F.
The​ y-intercept is minus1.

Answer 1

To analyze the given linear equation \( y = \frac{3}{4}x - 1 \), we can identify the slope and y-intercept directly from the equation, which is in slope-intercept form (\( y = mx + b \)).

1. Slope (m): The coefficient of \( x \) is the slope. In this case, the slope is \( \frac{3}{4} \).
2. Y-intercept (b): The constant term is the y-intercept. Here, the y-intercept is \( -1 \).

Now, let's evaluate each statement:

A. The y-intercept is three fourths.

• False; the y-intercept is actually \(-1\) not \(\frac{3}{4}\).

B. The line passes through the point (0, -3/4).

• False; when \( x = 0 \), \( y = -1 \), so the point is \( (0, -1) \).

C. The slope of the line is three fourths.

• True; as previously identified, the slope is \(\frac{3}{4}\).

D. The slope of the line is minus 1.

• False; the slope is \(\frac{3}{4}\), not \(-1\).

E. The line passes through the point (0, 1).

• False; when \( x = 0 \), \( y = -1\), not \(1\).

F. The y-intercept is minus 1.

• True; the y-intercept is indeed \(-1\).

Thus, the true statements are:

• C. The slope of the line is three fourths.
• F. The y-intercept is minus 1.