Xin graphs the equation y=4x – 6

Question

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Select all statements about Xin's graph that are true.

The line passes through the point (0, 6)
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The line passes through the point begin ordered pair 0 comma 6 end ordered pair .

The graph is a curved line.
The graph is a curved line.

The slope of the line is 4.
The slope of the line is 4.

The line passes through the origin.
The line passes through the origin.

The y-intercept of the line is –6
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Answer 1

To analyze the equation \(y = 4x - 6\), we can derive the following information:

1. The line passes through the point (0, 6): This statement is false. To find the y-intercept, where \(x = 0\), substitute \(0\) into the equation: \[ y = 4(0) - 6 = -6. \] So the line passes through the point \((0, -6)\).

2. The graph is a curved line: This statement is false. The given equation is linear, so the graph will be a straight line.

3. The slope of the line is 4: This statement is true. In the equation \(y = mx + b\), \(m\) represents the slope. Here, the slope \(m\) is 4.

4. The line passes through the origin: This statement is false. The line passes through the origin only if the y-intercept is 0. Since the y-intercept is \(-6\), the line does not pass through the origin.

5. The y-intercept of the line is –6: This statement is true. From the calculation above, we see that when \(x = 0\), \(y\) is indeed \(-6\), therefore the y-intercept is \(-6\).

Summary of True Statements:

• The slope of the line is 4.
• The y-intercept of the line is –6.

Summary of False Statements:

• The line passes through the point (0, 6).
• The graph is a curved line.
• The line passes through the origin.