Q. Find the x-intercept of the line (\(8x + 6y = 16\)).
Answer
Set \(y=0\) in the equation \(8x+6y=16\):
\[8x+6(0)=16\]
\[8x=16\]
\[x=2\]
Thus the x-intercept is \((2,0)\).
Detailed Explanation
Problem: Find the x-intercept of the line \(8x + 6y = 16\)
Step 1 – Definition
The x-intercept is the point where the graph crosses the x-axis, so on the x-axis \(y = 0\).
Step 2 – Substitute \(y = 0\)
\[
8x + 6(0) = 16
\]
Step 3 – Simplify and solve
\[
8x + 0 = 16 \\
8x = 16 \\
x = \frac{16}{8} = 2
\]
Answer
The x-intercept is the point \((2,0)\).
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FAQs
What is an x-intercept?
The x-intercept is the point where a graph crosses the x-axis, so the y-coordinate is zero. For a line, it’s the point ((x,0)) that satisfies the line’s equation.
How do I find the x-intercept of (8x+6y=16)?
Set (y=0): (8x+6(0)=16) gives (8x=16), so (x=2). The x-intercept is ((2,0)).
What is the y-intercept of (8x+6y=16)?
Set (x=0): (6y=16) so (y=tfrac{8}{3}). The y-intercept is ((0,tfrac{8}{3})).
How do I rewrite the equation in slope-intercept form?
Solve for (y): (6y=16-8x) so (y=-tfrac{4}{3}x+tfrac{8}{3}). This is (y=mx+b) with slope (m=-tfrac{4}{3}) and intercept (b=tfrac{8}{3}).
What is the slope of the line (8x+6y=16)?
From (y=-tfrac{4}{3}x+tfrac{8}{3}), the slope is (-tfrac{4}{3}). That means the line falls 4 units for every 3 units it moves right.
How can I graph this line quickly?
Plot the intercepts ((2,0)) and ((0,tfrac{8}{3})), then draw the line through them. Using intercepts gives two exact points for a straight line.
If coefficients share a common factor, should I simplify first?
Yes. Dividing by the greatest common divisor can make arithmetic easier. Here (8x+6y=16) can be divided by 2 to (4x+3y=8), which yields the same intercepts and slope.
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