Q. Find the x-intercept of the Line \( 3x + 20y = -24 \)

Answer

Understand what an x-intercept is.
The x-intercept is the point where the graph crosses the x-axis, so the y-coordinate there equals 0. In other words, set \(y = 0\).
Substitute \(y = 0\) into the equation.
Start with the given line: \(3x + 20y = -24\).
Replacing \(y\) with \(0\) gives \(3x + 20(0) = -24\).
Simplify the equation.
Compute \(20(0) = 0\), so the equation becomes \(3x = -24\).
Solve for \(x\).
Divide both sides of \(3x = -24\) by \(3\) to isolate \(x\). This uses the property that if \(a = b\) then \(\dfrac{a}{3} = \dfrac{b}{3}\).
Thus \(x = \dfrac{-24}{3} = -8\).
State the x-intercept as a point.
The x-intercept is the point \((-8, 0)\).

Final answer: The x-intercept is \((-8, 0)\).

Find x-intercepts with AI homework help.

AI helper

The x-intercept is the point where graph crosses the x-axis; its y-coordinate is 0.

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

Set x = 0: 20y = -24, so y = -24/20 = -6/5. The y-intercept is (0, -6/5).

Solve for y: 20y = -3x - 24, so y = (-3/20)x - 6/5.

The slope is -3/20; it means the line falls 3 units for every 20 units it moves right.

Plot (-8, 0) and (0, -6/5), then draw the straight line through those two points.

Substitute (-8, 0) into the original equation: 3(-8) + 20(0) = -24, which is true.

If the x-coefficient is 0, the equation is horizontal (y = constant). It has an x-intercept only if that constant is 0; otherwise no x-intercept.

Yes. Depending on coefficients and constants, x-intercepts can be integers, fractions, or decimals.

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