Q. Find the x- and y-intercepts of the line \(8x – 6y = 12\).

Q: How do you find the x-intercept of 8x-6y=12?.

Set y=0. Then 8x=12 giving x=\tfrac{3}{2}. The x-intercept is \big(\tfrac{3}{2},0\big).

Q: How do you find the y-intercept of 8x-6y=12? Do not use arrows.

Set x=0. Then -6y=12 so y=-2. The y-intercept is (0,-2).

Q: How do I write the equation in slope-intercept form?

Solve for y: -6y=12-8x so y=\tfrac{8}{6}x-\tfrac{12}{6}= \tfrac{4}{3}x-2. Thus y=\tfrac{4}{3}x-2.

Q: What is the slope of the line?

From y=\tfrac{4}{3}x-2, the slope is m=\tfrac{4}{3}. You can also compute slope from intercepts: \frac{-2-0}{0-\tfrac{3}{2}}=\tfrac{4}{3}..

Q: How do I graph the line using intercepts?

Plot the points \big(\tfrac{3}{2},0\big) and (0,-2) , then draw the straight line through them. Two points determine the line..

Q: How can I check an intercept is correct?

Substitute the point into 8x-6y=12. For \big(\tfrac{3}{2},0\big): 8\big(\tfrac{3}{2}\big)-6(0)=12. For (0,-2): 8(0)-6(-2)=12. Both hold.

Answer

\[
\text{If }y=0:\quad 8x=12,\ x=\tfrac{3}{2}\ \text{so the x-intercept is }(\tfrac{3}{2},0).
\]
\[
\text{If }x=0:\quad -6y=12,\ y=-2\ \text{so the y-intercept is }(0,-2).
\]

Detailed Explanation

Problem

Find the x- and y-intercepts of the line \(8x – 6y = 12\).

Explanation and step-by-step solution

Understanding interceptsThe x-intercept is the point where the line crosses the x-axis. At that point, the y-coordinate equals 0.
The y-intercept is the point where the line crosses the y-axis. At that point, the x-coordinate equals 0.
Find the x-intercept (set y = 0)Substitute y = 0 into the equation \(8x – 6y = 12\).
\(8x – 6(0) = 12\)

Simplify the left side: \(8x = 12\)

Solve for x by dividing both sides by 8: \(x = \dfrac{12}{8}\)

Simplify the fraction: \(x = \dfrac{3}{2}\)

Therefore the x-intercept is the point \(\left(\dfrac{3}{2},\,0\right)\).
Find the y-intercept (set x = 0)Substitute x = 0 into the equation \(8x – 6y = 12\).
\(8(0) – 6y = 12\)

Simplify the left side: \(-6y = 12\)

Solve for y by dividing both sides by -6: \(y = \dfrac{12}{-6}\)

Simplify the fraction: \(y = -2\)

Therefore the y-intercept is the point \((0,\,-2)\).

Final answer

x-intercept: \(\left(\dfrac{3}{2},\,0\right)\)
y-intercept: \((0,\,-2)\)

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Algebra FAQs

How do you find the x-intercept of \(8x-6y=12\)?.

Set \(y=0\). Then \(8x=12\) giving \(x=\tfrac{3}{2}\). The x-intercept is \(\big(\tfrac{3}{2},0\big)\).

How do you find the \(y\)-intercept of \(8x-6y=12\)? Do not use arrows.

Set \(x=0\). Then \(-6y=12\) so \(y=-2\). The y-intercept is \((0,-2)\).

How do I write the equation in slope-intercept form?

Solve for \(y\): \(-6y=12-8x\) so \(y=\tfrac{8}{6}x-\tfrac{12}{6}= \tfrac{4}{3}x-2\). Thus \(y=\tfrac{4}{3}x-2\).

What is the slope of the line?

From \(y=\tfrac{4}{3}x-2\), the slope is \(m=\tfrac{4}{3}\). You can also compute slope from intercepts: \(\frac{-2-0}{0-\tfrac{3}{2}}=\tfrac{4}{3}\)..

How do I graph the line using intercepts?

Plot the points \( \big(\tfrac{3}{2},0\big) \) and \( (0,-2) \), then draw the straight line through them. Two points determine the line..

What are the intercepts as decimals?

How can I check an intercept is correct?

Substitute the point into \(8x-6y=12\). For \(\big(\tfrac{3}{2},0\big)\): \(8\big(\tfrac{3}{2}\big)-6(0)=12\). For \((0,-2)\): \(8(0)-6(-2)=12\). Both hold.

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