Q. Find the x-intercept of the line \(3x + 20y = -12\).

Q: How do you find an x-intercept from an equation like 3x+20y=-12?.

Set y=0 and solve for x. For 3x+20(0)=-12 you get 3x=-12, so x=-4.

Q: How do you find the y-intercept of 3x+20y=-12?.

Set x=0 and solve: 20y=-12, so y=-12/20=-3/5. The y-intercept is -3/5.

Q: What is the slope of the line 3x+20y=-12?.

Solve for y: y=-\tfrac{3}{20}x-\tfrac{3}{5}. The slope is -\tfrac{3}{20}.

Q: How do you write the equation in slope-intercept form?

Rearrange: 20y=-3x-12 so y=-\tfrac{3}{20}x-\tfrac{3}{5}.

Q: Can an x-intercept be a fraction, and how should it be written?.

Can an x-intercept be a fraction, and how should it be written?.

Q: How can I graph this line using intercepts?

Plot the x-intercept -4,0 and y-intercept 0,-\frac{3}{5} , then draw the straight line through those two points.

Q: How do I check my x-intercept is correct?

Substitute x=-4 and y=0 into 3x+20y=-12: 3(-4)+20(0)=-12. The equation holds, so it’s correct.

Q: What common mistakes should I avoid?

Don’t forget to set y=0 for the x-intercept, watch sign errors when solving, and simplify fractions fully.

Answer

Set \(y=0\): \(3x=-12\), so \(x=-4\). Final answer: \(-4\)

Detailed Explanation

Definition: an x-intercept is a point where the graph crosses the x-axis, so the y-coordinate is 0. Set \(y = 0\).
Substitute \(y = 0\) into the equation \(3x + 20y = -12\):
\(3x + 20(0) = -12\).
Simplify the left side: \(3x + 0 = -12\), so \(3x = -12\).
Solve for \(x\) by dividing both sides by 3:
\(x = \dfrac{-12}{3} = -4\).
Final answer: the x-intercept is \(-4\).

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Algebra FAQs

How do you find an x-intercept from an equation like \(3x+20y=-12\)?.

Set \(y=0\) and solve for \(x\). For \(3x+20(0)=-12\) you get \(3x=-12\), so \(x=-4\).

What is the x-intercept for \(3x+20y=-12\)?

The x-intercept is \(-4\)..

How do you find the y-intercept of \(3x+20y=-12\)?.

Set \(x=0\) and solve: \(20y=-12\), so \(y=-12/20=-3/5\). The \(y\)-intercept is \(-3/5\).

What is the slope of the line \(3x+20y=-12\)?.

Solve for \(y\): \(y=-\tfrac{3}{20}x-\tfrac{3}{5}\). The slope is \(-\tfrac{3}{20}\).

How do you write the equation in slope-intercept form?

Rearrange: \(20y=-3x-12\) so \(y=-\tfrac{3}{20}x-\tfrac{3}{5}\).

Can an \(x\)-intercept be a fraction, and how should it be written?.

How can I graph this line using intercepts?

Plot the x-intercept \( -4,0 \) and y-intercept \( 0,-\frac{3}{5} \), then draw the straight line through those two points.

How do I check my \(x\)-intercept is correct?

Substitute \(x=-4\) and \(y=0\) into \(3x+20y=-12\): \(3(-4)+20(0)=-12\). The equation holds, so it’s correct.

What common mistakes should I avoid?

Don’t forget to set \(y=0\) for the x-intercept, watch sign errors when solving, and simplify fractions fully.

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