Q. Find the slope of the line \(y=12x+6\).

Q: What is the slope of the line y=12x+6?

The slope is the coefficient of x; here the slope is 12.

Q: How do I read slope from slope-intercept form y=mx+b?

In y=mx+b, m is the slope and b the y-intercept. For y=12x+6, m=12 and b=6.

Q: How do I find the slope given two points (x_1,y_1) and (x_2,y_2)?

Use m=\frac{y_2-y_1}{x_2-x_1}. That quotient gives the rise over run between the two points.

Q: How do I get the slope from standard form Ax+By=C?

Solve for y or use the formula: slope m=-\frac{A}{B}. For example, 2x+3y=6 has slope -\frac{2}{3}.

Q: What is the slope of a line parallel to y=12x+6?

Any parallel line has the same slope: 12.

Q: What is the slope of a line perpendicular to y=12x+6?

What is the slope of a line perpendicular to y=12x+6?

Q: What are the intercepts of y=12x+6?

The y-intercept is 6 at (0,6). The x-intercept solves 0=12x+6, giving x=-\frac{1}{2}, point \left(-\frac{1}{2},0\right).

Answer

\(y=12x+6\) is in slope-intercept form \(y=mx+b\), so the slope \(m=12\).

Detailed Explanation

Problem

Find the slope of the line given by the equation

\(y = 12x + 6\)

Step-by-step solution

Recall the slope-intercept form of a line:

\(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Compare the given equation \(y = 12x + 6\) with the slope-intercept form. The coefficient of \(x\) corresponds to the slope \(m\).

Therefore, \(m = 12\).
As a verification, compute the slope as rise over run between two points on the line. Choose \(x_1 = 0\), then \(y_1 = 12(0) + 6 = 6\), giving point \((0,6)\). Choose \(x_2 = 1\), then \(y_2 = 12(1) + 6 = 18\), giving point \((1,18)\).

Compute the slope:

\(m = \dfrac{y_2 – y_1}{x_2 – x_1} = \dfrac{18 – 6}{1 – 0} = \dfrac{12}{1} = 12\).
Interpretation: a slope of 12 means that for every increase of 1 in \(x\), \(y\) increases by 12 units.

Answer

The slope of the line \(y = 12x + 6\) is 12.

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FAQs

What is the slope of the line \(y=12x+6\)?

The slope is the coefficient of \(x\); here the slope is \(12\).

How do I read slope from slope-intercept form \(y=mx+b\)?

In \(y=mx+b\), \(m\) is the slope and \(b\) the y-intercept. For \(y=12x+6\), \(m=12\) and \(b=6\).

How do I find the slope given two points \((x_1,y_1)\) and \((x_2,y_2)\)?

Use \(m=\frac{y_2-y_1}{x_2-x_1}\). That quotient gives the rise over run between the two points.

How do I get the slope from standard form \(Ax+By=C\)?

Solve for \(y\) or use the formula: slope \(m=-\frac{A}{B}\). For example, \(2x+3y=6\) has slope \(-\frac{2}{3}\).

What is the slope of a line parallel to \(y=12x+6\)?

Any parallel line has the same slope: \(12\).

What is the slope of a line perpendicular to \(y=12x+6\)?

What does a positive slope like \(12\) mean graphically?

positive slope means the line rises left to right; here it rises 12 units for each 1 unit moved to the right (very steep).

What are the intercepts of \(y=12x+6\)?

The y-intercept is 6 at \((0,6)\). The x-intercept solves \(0=12x+6\), giving \(x=-\frac{1}{2}\), point \(\left(-\frac{1}{2},0\right)\).

Slope of y=12x+6 is 12; use tools ok.
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Q. Find the slope of the line \(y=12x+6\).

Answer

Detailed Explanation

Problem

Step-by-step solution

Answer

FAQs

What is the slope of the line \(y=12x+6\)?

How do I read slope from slope-intercept form \(y=mx+b\)?

How do I find the slope given two points \((x_1,y_1)\) and \((x_2,y_2)\)?

How do I get the slope from standard form \(Ax+By=C\)?

What is the slope of a line parallel to \(y=12x+6\)?

What is the slope of a line perpendicular to \(y=12x+6\)?

What does a positive slope like \(12\) mean graphically?

What are the intercepts of \(y=12x+6\)?

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