Q. Find the x-intercept of the line \(2x – 4y = -12\).
Answer
To find the x-intercept, set \(y=0\):
\[
\begin{aligned}
2x-4(0) &= -12 \\
2x &= -12 \\
x &= -6
\end{aligned}
\]
The x-intercept is \((-6, 0)\).
Detailed Explanation
Problem: Find the x-intercept of the line given by the equation
\(2x – 4y = -12\).
\(2x – 4y = -12\).
Step 1 – Understand what an x-intercept is
The x-intercept is the point where the graph crosses the x-axis. At any point on the x-axis the y-coordinate equals 0. Therefore set \(y = 0\) in the equation.
Step 2 – Substitute \(y = 0\) into the equation
\[
2x – 4(0) = -12
\]
Simplify the expression:
\[
2x = -12
\]
Step 3 – Solve for \(x\)
Divide both sides by 2:
\[
x = \frac{-12}{2} = -6
\]
Answer
The x-intercept is the point \((-6, 0)\).
See full solution
Graph
FAQs
How do I find the x-intercept of (2x-4y=-12)?
Set (y=0). Then (2x=-12) so (x=-6). The x-intercept is ((-6,0)).
How do I find the y-intercept of (2x-4y=-12)?
Set (x=0). Then (-4y=-12) so (y=3). The y-intercept is ((0,3)).
How do I write the equation in slope-intercept form?
Solve for \(y\): \(-4y = -2x - 12\) so \(y = \frac{1}{2}x + 3\).
What is the slope of the line?
From \(y = \frac{1}{2}x + 3\), the slope is \(m = \frac{1}{2}\).
How can I graph the line quickly?
Plot the intercepts ((-6,0)) and ((0,3)), then draw the straight line through them.
Can the equation be simplified?
Can the equation be simplified?
What is the intercept form of the line?
Using intercepts \(a=-6\), \(b=3\): \(\frac{x}{-6} + \frac{y}{3} = 1\).
How can I check the x-intercept is correct?
Substitute ((-6,0)) into (2x-4y=-12): (2(-6)-4(0)=-12), which is true.
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