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 \(x=\frac{15}{20}=\frac{3}{4}\). The x-intercept is \(\left(\frac{3}{4},0\right)\).
How do you find the y-intercept of (20x-17y=15)?
Set \(x=0\), so \(-17y = 15\). Then \(y = -\frac{15}{17}\). The y-intercept is \(\left(0, -\frac{15}{17}\right)\).
How do you convert (20x-17y=15) to slope-intercept form?
Solve for \(y\): \(-17y = 15 - 20x\) so \(y = \frac{20x - 15}{17}\). In slope-intercept form: \(y = \frac{20}{17}x - \frac{15}{17}\).
What is the slope of the line (20x-17y=15)?
The slope is the coefficient of \(x\) in slope-intercept form, \(\frac{20}{17}\).
Does the x-intercept equal \(\frac{15}{20}\) and can it be simplified?
Yes. \(\frac{15}{20} = \frac{3}{4}\) after dividing numerator and denominator by 5.
How can I quickly graph this line?
How can I quickly graph this line?
For a general standard form (Ax+By=C), how do you find intercepts?
x-intercept: set \(y=0\) giving \(x=\frac{C}{A}\) if \(A \neq 0\). y-intercept: set \(x=0\) giving \(y=\frac{C}{B}\) if \(B \neq 0\).
How can I check that \(\left(\frac{3}{4}, 0\right)\) is correct?
Substitute into the equation: \(20 \cdot \frac{3}{4} - 17 \cdot 0 = 15\). Left side equals 15, so the point satisfies the equation.
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