Q. Find the x-intercept of the line (\(20x – 17y = 15\)).
Answer
To find the x-intercept of the line \(20x-17y=15\), set \(y=0\):
\[20x-17(0)=15\]
\[20x=15\]
\[x=\frac{15}{20}=\frac{3}{4}\]
The x-intercept is \(\boxed{\left(\frac{3}{4},0\right)}\).
Detailed Explanation
Problem: Find the x-intercept of the line given by the equation \(20x-17y=15\).
Step 1 — Understand what the x-intercept means
The x-intercept is the point where the graph crosses the x-axis. At any point on the x-axis the y-coordinate is 0. Therefore set \(y=0\) in the equation and solve for \(x\).
Step 2 — Substitute \(y=0\) into the equation
\[
20x-17\cdot 0=15
\]
Simplify:
\[
20x=15
\]
Step 3 — Solve for \(x\)
Divide both sides by 20:
\[
x=\frac{15}{20}
\]
Simplify the fraction by dividing numerator and denominator by 5:
\[
x=\frac{3}{4}
\]
Answer
\[
\left(\frac{3}{4},\,0\right)
\]
See full solution
Graph
FAQs
How do you find the x-intercept of (20x-17y=15)?
Set (y=0), so (20x=15). Then (x=dfrac{15}{20}=dfrac{3}{4}). The x-intercept is (left(dfrac{3}{4},0right)).
How do you find the y-intercept of (20x-17y=15)?
Set (x=0), so (-17y=15). Then (y=-dfrac{15}{17}). The y-intercept is (left(0,-dfrac{15}{17}right)).
How do you convert (20x-17y=15) to slope-intercept form?
Solve for (y): (-17y=15-20x) so (y=dfrac{20x-15}{17}). In slope-intercept form: (y=dfrac{20}{17}x-dfrac{15}{17}).
What is the slope of the line (20x-17y=15)?
The slope is the coefficient of (x) in slope-intercept form, (dfrac{20}{17}).
Does the x-intercept equal (dfrac{15}{20}) and can it be simplified?
Yes. (dfrac{15}{20}=dfrac{3}{4}) after dividing numerator and denominator by 5.
How can I quickly graph this line?
Plot the intercepts (left(dfrac{3}{4},0right)) and (left(0,-dfrac{15}{17}right)), then draw the line through them. Use equal scaling on axes for accuracy.
For a general standard form (Ax+By=C), how do you find intercepts?
x-intercept: set (y=0) giving (x=dfrac{C}{A}) if (Aneq0). y-intercept: set (x=0) giving (y=dfrac{C}{B}) if (Bneq0).
How can I check that (left(dfrac{3}{4},0right)) is correct?
Substitute into the equation: (20!cdot!dfrac{3}{4}-17!cdot!0=15). Left side equals (15), so the point satisfies the equation.
Find new AI helpers now.
Start saving time today
Start saving time today
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