Q. Find the x- and y-intercepts of the graph of \(-2x+4y=12\). State each answer as an integer or an improper fraction in simplest form.

Q: How do I find the x-intercept of -2x+4y=12 ?.

Set y=0 and solve -2x+4(0)=12 \Rightarrow -2x=12 \Rightarrow x=-6 . The x-intercept is (-6,0) ..

Q: How do I find the y-intercept of -2x+4y=12 ?

Set x=0 and solve -2(0)+4y=12 \Rightarrow 4y=12 \Rightarrow y=3 . The y-intercept is (0,3) .

Q: What is the slope of the line -2x+4y=12 ?

Solve for y : 4y=2x+12 \Rightarrow y=\tfrac{1}{2}x+3 . The slope is \tfrac{1}{2} .

Q: How do I graph the line using intercepts?

Plot the intercepts (-6,0) and (0,3) , then draw the straight line through them. Two points uniquely determine the line.

Q: How can I check my intercepts are correct?

Substitute each point into -2x+4y=12 . For (-6,0) : -2(-6)+4(0)=12 . For (0,3) : -2(0)+4(3)=12 . Both satisfy the equation.

Q: How does the standard form Ax+By=C make finding intercepts easier?

For Ax+By=C, x-intercept: set y=0 and solve Ax=C. y-intercept: set x=0 and solve By=C. This gives intercepts directly as \bigl(\tfrac{C}{A},0\bigr) and \bigl(0,\tfrac{C}{B}\bigr) when A,B\neq0.

Answer

For the x-intercept set \(y=0\): \(-2x+4(0)=12\), so \(-2x=12\) and \(x=-6\). For the y-intercept set \(x=0\): \(-2(0)+4y=12\), so \(4y=12\) and \(y=3\).

x-intercept: \((-6,0)\). y-intercept: \((0,3)\).

Detailed Explanation

Goal: Find the x-intercept and y-intercept of the line given by the equation \( -2x + 4y = 12 \).

x-intercept (point where the graph crosses the x-axis)

By definition, an x-intercept occurs where \(y=0\).
Substitute \(y=0\) into the equation: \( -2x + 4(0) = 12\).
Simplify: \( -2x + 0 = 12\), so \( -2x = 12\).
Solve for \(x\) by dividing both sides by \(-2\): \( x = \frac{12}{-2} = -6\).
Therefore the x-intercept is the point \((-6,\,0)\).

y-intercept (point where the graph crosses the y-axis)

By definition, a y-intercept occurs where \(x=0\).
Substitute \(x=0\) into the equation: \( -2(0) + 4y = 12\).
Simplify: \( 0 + 4y = 12\), so \( 4y = 12\).
Solve for \(y\) by dividing both sides by \(4\): \( y = \frac{12}{4} = 3\).
Therefore the y-intercept is the point \((0,\,3)\).

Final answers: x-intercept: \((-6,\,0)\). y-intercept: \((0,\,3)\).

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Algebra FAQs

How do I find the x-intercept of \( -2x+4y=12 \)?.

Set \( y=0 \) and solve \( -2x+4(0)=12 \Rightarrow -2x=12 \Rightarrow x=-6 \). The x-intercept is \( (-6,0) \)..

How do I find the y-intercept of \( -2x+4y=12 \)?

Set \( x=0 \) and solve \( -2(0)+4y=12 \Rightarrow 4y=12 \Rightarrow y=3 \). The y-intercept is \( (0,3) \).

What is the slope of the line \( -2x+4y=12 \)?

Solve for \( y \): \( 4y=2x+12 \Rightarrow y=\tfrac{1}{2}x+3 \). The slope is \( \tfrac{1}{2} \).

How do I graph the line using intercepts?

Plot the intercepts \( (-6,0) \) and \( (0,3) \), then draw the straight line through them. Two points uniquely determine the line.

How can I check my intercepts are correct?

Substitute each point into \( -2x+4y=12 \). For \( (-6,0) \): \( -2(-6)+4(0)=12 \). For \( (0,3) \): \( -2(0)+4(3)=12 \). Both satisfy the equation.

If an intercept were a fraction, how should it be presented?

How does the standard form \(Ax+By=C\) make finding intercepts easier?

For \(Ax+By=C\), x-intercept: set \(y=0\) and solve \(Ax=C\). y-intercept: set \(x=0\) and solve \(By=C\). This gives intercepts directly as \(\bigl(\tfrac{C}{A},0\bigr)\) and \(\bigl(0,\tfrac{C}{B}\bigr)\) when \(A,B\neq0\).

Solve for intercepts:x-intercept: set y = 0 → -2x = 12 → x = -6, so x-intercept = (-6, 0). y-intercept: set x = 0 → 4y = 12 → y = 3, so y-intercept = (0, 3).Get fast help with your homework now.
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