Q. Find the x-intercept of the line \(9x – 3y = 24\).
Answer
Set \(y = 0\):
\[ 9x – 3(0) = 24 \]
\[ 9x = 24 \]
\[ x = \frac{24}{9} = \frac{8}{3} \]
Final result: \(\boxed{\left(\frac{8}{3}, 0\right)}\)
Detailed Explanation
Problem: Find the x-intercept of the line \(9x-3y=24\).
Step 1 — Use the definition of an x-intercept
The x-intercept is the point where the line crosses the x-axis, so \(y=0\).
Step 2 — Substitute \(y=0\) into the equation
\[ 9x-3(0)=24 \]
Step 3 — Simplify
\[ 9x=24 \]
Step 4 — Solve for \(x\)
\[ x=\frac{24}{9} \]
Step 5 — Reduce the fraction
Both 24 and 9 are divisible by 3:
\[ 24\div 3=8, \qquad 9\div 3=3 \]
so
\[ x=\frac{8}{3} \]
Answer
The x-intercept is \(x=\tfrac{8}{3}\), which as a point is \(\bigl(\tfrac{8}{3}, \, 0\bigr)\).
See full solution
Graph
FAQs
How do I find the x-intercept of the line (9x-3y=24)?
Set \(y=0\) and solve: \(9x-3(0)=24\), so \(9x=24\) and \(x=\frac{24}{9}=\frac{8}{3}\). The x-intercept is \(\left(\frac{8}{3},0\right)\).
How do I find the y-intercept?
Set (x=0): (9(0)-3y=24) so (-3y=24) and (y=-8). The y-intercept is ((0,-8)).
What is the slope of the line?
Rewrite to slope-intercept form: (9x-3y=24), (3y=9x-24), (y=3x-8). The slope is (3).
How can I simplify the equation first?
Divide every term by (3): (3x-y=8). This simpler form makes intercepts or slope easier to find.
How can I check the x-intercept is correct?
Substitute \(x = \frac{8}{3}\) and \(y = 0\): \(9\left(\frac{8}{3}\right) - 3(0) = 24\), which gives \(24 = 24\), so the point is correct.
How to write the line in intercept form?
How to write the line in intercept form?
How do I graph the line using intercepts?
Plot the intercepts \(\left(\frac{8}{3}, 0\right)\) and \((0,-8)\), then draw the straight line through them. Two points determine the line.
Discover smart tools for you.
Start right away.
Start right away.
173,935+ happy customers
Math, Calculus, Geometry, etc.
Math, Calculus, Geometry, etc.
Unlimited AI homework help 
Diagram Generator, Flashcard Maker, Notes Generator, Research Assistant, Answer Generator, AI Homework Helper & AI Detector