Q. Find the x-intercept of the line \( 7x – 17y = -28 \)

Answer

Set y to 0.
\[ 7x – 17(0) = -28 \]
Solve for x.
\[ 7x = -28 \]

\[ x = -4 \]
State the x-intercept.
\[ (-4, 0) \]

Detailed Explanation

Solution — find the x-intercept of the line

Recall the definition: The x-intercept is the point where the line crosses the x-axis, so the y-coordinate is 0. Therefore set y = 0 in the equation of the line.
Substitute y = 0 into the equation:

\(7x – 17(0) = -28\)

Since \(17(0)=0\), this simplifies to

\(7x = -28\).
Solve for x:

Divide both sides by 7:

\(x = \dfrac{-28}{7} = -4\).
State the x-intercept as an ordered pair:

The x-intercept is \((-4, 0)\).
Optional check:

Substitute \(x=-4\) and \(y=0\) into the original equation:

\(7(-4) – 17(0) = -28 – 0 = -28\), which matches the right-hand side, so the solution is correct.

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Frequently Asked Questions

What is the x-intercept of 7x - 17y = -28?

Set y = 0: 7x = -28, so x = -4. The x-intercept is (-4, 0).

How do you find an x-intercept in general?

Set y = 0 in the equation and solve for x. For ax + by = c, x = c/(if ≠ 0).

How do I find the y-intercept of this line?

Set x = 0: -17y = -28, so y = 28/17. The y-intercept is (0, 28/17).

What is the slope of the line?

Rewrite: y = (7/17)x + 28/17. The slope is 7/17.

How can I graph this line quickly?

Plot the intercepts (-4,0) and (0,28/17 ≈ 1.647) and draw the straight line through them.

How can I check that my x-intercept is correct?

Substitute (-4,0) into the equation: 7(-4) - 17(0) = -28, which is true, so the intercept is correct.

Can line fail to have an x-intercept?

Yes. Horizontal lines y = k with k ≠ 0 have no x-intercept. Vertical lines x = always have an x-intercept at (a,0).

When is the formulx = c/invalid for intercepts?

It fails if = 0 (no x term). Then if equation is 0x + by = c, either no solution or y = c/b (horizontal line), so no x-intercept unless c = 0 (the whole x-axis).

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