Q. What is the y-intercept of \(3x + y = 12\)?

Q: What is the y-intercept of 3x + y = 12?

Set x=0. Then y=12. The y-intercept point is (0,12) and the y-value is 12.

Q: How do you find the y-intercept from standard form Ax + By = C?

Set x=0 and solve for y. You get y = C/B. The intercept point is (0, C/B) (provided B \neq 0).

Q: How do you convert 3x + y = 12 to slope-intercept form?

Solve for y: y = -3x + 12. This is slope-intercept form y = mx + b with m = -3 and b = 12.

Q: What is the slope of the line 3x + y = 12?

From y = -3x + 12, the slope is m = -3.

Q: What is the x-intercept of 3x + y = 12?

Set y=0. Then 3x = 12, so x = 4. The x-intercept is (4,0).

Q: How can I graph 3x + y = 12 quickly using intercepts?

How can I graph 3x + y = 12 quickly using intercepts?

Q: Does the point (2,6) lie on 3x + y = 12?

Plug in x=2: 3(2)+y=12 gives 6+y=12 so y=6. Yes, (2,6) lies on the line.

Q: What does the y-intercept represent in context?

The y-intercept (0,12) is where the line crosses the y-axis: the value of y when x=0. It’s the constant term b in y=mx+b.

Answer

Set x=0: \(3(0)+y=12\), so \(y=12\). The y-intercept is \((0,12)\).

Detailed Explanation

Find the y-intercept of the equation

We are given the linear equation

\[ 3x + y = 12 \]

Definition (what to do):

The y-intercept is the point where the graph crosses the y-axis. At every point on the y-axis, the x-coordinate is 0. Therefore, to find the y-intercept, set x equal to 0 in the equation and solve for y.
Substitute x = 0 into the equation (step-by-step):

Replace x with 0 in the equation:

\[ 3(0) + y = 12 \]
Simplify the expression (step-by-step):

Compute 3 times 0:

\[ 0 + y = 12 \]

Then simplify the left side:

\[ y = 12 \]
Write the y-intercept as a coordinate (what to do):

The y-intercept point has x = 0 and the y-value found above, so the y-intercept is

\[ (0,\,12) \]

Often the y-intercept is also reported as the y-coordinate 12.

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FAQs

What is the y-intercept of \(3x + y = 12\)?

Set \(x=0\). Then \(y=12\). The y-intercept point is \((0,12)\) and the y-value is \(12\).

How do you find the y-intercept from standard form \(Ax + By = C\)?

Set \(x=0\) and solve for \(y\). You get \(y = C/B\). The intercept point is \((0, C/B)\) (provided \(B \neq 0\)).

How do you convert \(3x + y = 12\) to slope-intercept form?

Solve for \(y\): \(y = -3x + 12\). This is slope-intercept form \(y = mx + b\) with \(m = -3\) and \(b = 12\).

What is the slope of the line \(3x + y = 12\)?

From \(y = -3x + 12\), the slope is \(m = -3\).

What is the x-intercept of \(3x + y = 12\)?

Set \(y=0\). Then \(3x = 12\), so \(x = 4\). The x-intercept is \((4,0)\).

How can I graph \(3x + y = 12\) quickly using intercepts?

Does the point \((2,6)\) lie on \(3x + y = 12\)?

Plug in \(x=2\): \(3(2)+y=12\) gives \(6+y=12\) so \(y=6\). Yes, \((2,6)\) lies on the line.

What does the y-intercept represent in context?

The y-intercept \((0,12)\) is where the line crosses the y-axis: the value of \(y\) when \(x=0\). It’s the constant term \(b\) in \(y=mx+b\).

Find the y-intercept by setting x=0.
The y-intercept is 12.

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