Q. What is the \(x\)-intercept of the line \(6x – 3y = 24\)? The x-intercept is \(4\).

Q: What is the x-intercept of the line 6x - 3y = 24?

Set y=0. 6x=24 so x=4. The x-intercept is (4,0).

Q: How do you find the y-intercept of 6x - 3y = 24?.

Set x=0: -3y=24 so y=-8. The y-intercept is (0,-8).

Q: How do I rewrite 6x - 3y = 24 in slope-intercept form?

Solve for y : -3y = 24 - 6x so y = 2x - 8 . That is the slope-intercept form.

Q: What is the intercept form of the equation?

Divide by 24: \frac{x}{4} - \frac{y}{8} = 1 . Intercepts are a = 4 and b = -8 (y-intercept negative).

Q: Does substituting x=4 and y=0 satisfy the equation?

Yes: 6(4)-3(0)=24 simplifies to 24=24, so (4,0) lies on the line.

Answer

Set \(y=0\): \(6x-3(0)=24\) so \(6x=24\), \(x=4\). x-intercept = \((4,0)\)

Detailed Explanation

Find the x-intercept of the line 6x − 3y = 24

Understand what the x-intercept means.The x-intercept is the point where the graph of the line crosses the x-axis. At any point on the x-axis, the y-coordinate is 0. Therefore to find the x-intercept set y equal to 0 in the equation of the line.
Substitute y = 0 into the equation.Start with the given equation:
\(6x – 3y = 24\).Replace y with 0:
\(6x – 3(0) = 24\).
Simplify the equation after substitution.Evaluate the term involving 0:
\(6x – 0 = 24\).This simplifies to:
\(6x = 24\).
Solve for x.Divide both sides of the equation by 6 to isolate x:
\(x = \dfrac{24}{6}\).Compute the division:
\(x = 4\).
Write the x-intercept as a coordinate point.The x-intercept corresponds to the point where x = 4 and y = 0, so the x-intercept is the point
\((4, 0)\).

Answer: x-intercept = 4 (point is (4, 0))

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Algebra FAQs

What is the x-intercept of the line \(6x - 3y = 24\)?

Set \(y=0\). \(6x=24\) so \(x=4\). The \(x\)-intercept is \((4,0)\).

Why do we set \(y=0\) to find the \(x\)-intercept?

The x-intercept is where the graph crosses the x-axis; every point on the x-axis has \(y=0\), so solving with \(y=0\) gives the x-coordinate of that crossing.

How do you find the y-intercept of \(6x - 3y = 24\)?.

Set \(x=0\): \(-3y=24\) so \(y=-8\). The y-intercept is \((0,-8)\).

How do I rewrite \(6x - 3y = 24\) in slope-intercept form?

Solve for \( y \): \(-3y = 24 - 6x\) so \( y = 2x - 8 \). That is the slope-intercept form.

What is the slope of the line \(6x - 3y = 24\)?.

From \(y=2x-8\) the slope is \(m=2\).

How can I quickly graph this line?

What is the intercept form of the equation?

Divide by 24: \( \frac{x}{4} - \frac{y}{8} = 1 \). Intercepts are \( a = 4 \) and \( b = -8 \) (y-intercept negative).

Does substituting \(x=4\) and \(y=0\) satisfy the equation?

Yes: \(6(4)-3(0)=24\) simplifies to \(24=24\), so \((4,0)\) lies on the line.

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