Q. Find the slope of the line \(y = \frac{3}{4}x + 14\).

Q: What is the y-intercept?

The y-intercept is b=14, which gives the point (0,14).

Q: What is the x-intercept?

Set y=0: 0 = \frac{3}{4}x + 14 so x = -\frac{56}{3}. The x-intercept is \left(-\frac{56}{3}, 0\right).

Q: What is the equation of a line parallel to this one?

Parallel lines share slope m = \frac{3}{4}. General form: y = \frac{3}{4}x + c. Example through origin: y = \frac{3}{4}x.

Q: What is the slope of a line perpendicular to this one?

Perpendicular slope is the negative reciprocal: -\frac{4}{3}. Example: y = -\frac{4}{3}x.

Q: How to graph it quickly?

Start at (0,14). Use slope rise/run 3 up, 4 right to plot another point, then draw the line through them.

Q: How to express it in point-slope form?

Using (0,14): y-14 = \frac{3}{4}(x-0).

Answer

The equation is in slope–intercept form \(y = mx + b\), so the slope \(m = \frac{3}{4}\). Final result: \(\frac{3}{4}\).

Detailed Explanation

Problem: Find the slope of the line \(y = \tfrac{3}{4}x + 14\).

Recall the slope-intercept form.

The slope-intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Compare the given equation to the form.

The given equation is \(y = \tfrac{3}{4}x + 14\). In this form, the coefficient multiplying \(x\) corresponds to \(m\), the slope.
Identify the slope.

Comparing term-by-term, the coefficient of \(x\) is \(\tfrac{3}{4}\), so the slope is \(m = \tfrac{3}{4}\).
Interpretation (optional).

The slope \(\tfrac{3}{4}\) means that for every 4 units you move to the right along the x-axis, the line rises 3 units (rise/run = 3/4). In decimal form the slope is \(0.75\).

Answer: The slope is \(\tfrac{3}{4}\).

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FAQs

What is the slope of the line \(y=\frac{3}{4}x+14\)?

The slope is \(m=\frac{3}{4}\).

What is the y-intercept?

The y-intercept is \(b=14\), which gives the point \((0,14)\).

What is the x-intercept?

Set \(y=0\): \(0 = \frac{3}{4}x + 14\) so \(x = -\frac{56}{3}\). The x-intercept is \(\left(-\frac{56}{3}, 0\right)\).

What is the equation of a line parallel to this one?

Parallel lines share slope \(m = \frac{3}{4}\). General form: \(y = \frac{3}{4}x + c\). Example through origin: \(y = \frac{3}{4}x\).

What is the slope of a line perpendicular to this one?

Perpendicular slope is the negative reciprocal: \(-\frac{4}{3}\). Example: \(y = -\frac{4}{3}x\).

How do I write this line in standard form?

How to graph it quickly?

Start at \((0,14)\). Use slope rise/run \(3\) up, \(4\) right to plot another point, then draw the line through them.

How to express it in point-slope form?

Using \((0,14)\): \(y-14 = \frac{3}{4}(x-0)\).

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