Q. In the xy-plane, the slope of the line \(y = m x – 4\).

Q: What is the slope of the line y=mx-4?

The slope is m; in slope-intercept form y=mx+b, the coefficient of x is the slope.

Q: What is the y-intercept of y=mx-4?

The y-intercept is (0,-4) because when x=0, y=-4.

Q: How do I find the x-intercept of y=mx-4?

Set y=0: 0=mx-4 so x=\frac{4}{m}, provided m\neq0. If m=0 there is no x-intercept (horizontal line y=-4).

Q: What is the slope of a line parallel to y=mx-4?

Any line parallel has the same slope m. Parallel lines share equal slopes.

Q: What is the slope of a line perpendicular to y=mx-4?

The perpendicular slope is -\frac{1}{m}, for m\neq0. If m=0 the perpendicular line is vertical (undefined slope).

Q: How do I find m if the line passes through a point (x_1,y_1)?

How do I find m if the line passes through a point (x_1,y_1)?

Q: What happens when m=0 in y=mx-4?

The line becomes y=-4, a horizontal line with slope 0 and no change in y as x varies.

Q: How is the slope m related to the angle the line makes with the x-axis?

The slope equals \tan\theta, where \theta is the angle above the positive x-axis; \theta=\arctan(m) (principal value).

Answer

The equation is in slope–intercept form \(y=mx-4\), so the slope is \(m\).

Detailed Explanation

We are given the equation of a line in the xy-plane:

Recall the slope-intercept form of a line:
\(y = mx + b\), where the slope is the coefficient of \(x\) and the y-intercept is \(b\).
Compare the given equation
\(y = mx – 4\)
to the slope-intercept form. The coefficient of \(x\) in the given equation is \(m\), and the constant term \(-4\) is the y-intercept.
Therefore, by definition of slope in the slope-intercept form, the slope of the line is

\(m\)

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FAQs

What is the slope of the line \(y=mx-4\)?

The slope is \(m\); in slope-intercept form \(y=mx+b\), the coefficient of \(x\) is the slope.

What is the y-intercept of \(y=mx-4\)?

The y-intercept is \((0,-4)\) because when \(x=0\), \(y=-4\).

How do I find the x-intercept of \(y=mx-4\)?

Set \(y=0\): \(0=mx-4\) so \(x=\frac{4}{m}\), provided \(m\neq0\). If \(m=0\) there is no x-intercept (horizontal line \(y=-4\)).

What is the slope of a line parallel to \(y=mx-4\)?

Any line parallel has the same slope \(m\). Parallel lines share equal slopes.

What is the slope of a line perpendicular to \(y=mx-4\)?

The perpendicular slope is \(-\frac{1}{m}\), for \(m\neq0\). If \(m=0\) the perpendicular line is vertical (undefined slope).

How do I find \(m\) if the line passes through a point \((x_1,y_1)\)?

What happens when \(m=0\) in \(y=mx-4\)?

The line becomes \(y=-4\), a horizontal line with slope \(0\) and no change in \(y\) as \(x\) varies.

How is the slope \(m\) related to the angle the line makes with the x-axis?

The slope equals \(\tan\theta\), where \(\theta\) is the angle above the positive x-axis; \(\theta=\arctan(m)\) (principal value).

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