Q. Find the x-intercept of the line \(8x+14y=15\).

Q: What is the x-intercept of the line 8x+14y=15?

Set y=0 and solve 8x=15. So x=\frac{15}{8} and the x-intercept is \left(\frac{15}{8},0\right).

Q: What is the y-intercept of the same line?

Set x=0: 14y = 15 so y = \frac{15}{14}. The y-intercept is \left(0, \frac{15}{14}\right).

Q: What is the slope of the line 8x+14y=15?

Rearranged: y = -\frac{4}{7}x + \frac{15}{14}. The slope is -\frac{4}{7}.

Q: How can I graph this line quickly?

Plot the intercepts \left(\frac{15}{8}, 0\right) and \left(0, \frac{15}{14}\right), then draw the straight line through them. Two points determine a line.

Answer

Set y = 0:
\[8x + 14(0) = 15\]
\[8x = 15\]
\[x = \frac{15}{8} = 1.875\]

Detailed Explanation

Find the x-intercept of the line 8x + 14y = 15 — step-by-step

Understand what the x-intercept is
The x-intercept is the point where the graph crosses the x-axis, so the y-coordinate is 0. In symbols: set \(y = 0\).
Substitute y = 0 into the equation
Replace y with 0 in the equation \(8x + 14y = 15\), giving

\(8x + 14\cdot 0 = 15\)
Simplify the equation
Compute the product \(14\cdot 0 = 0\), so the equation becomes

\(8x = 15\)
Solve for x
Divide both sides by 8 to isolate x:

\(x = \dfrac{15}{8}\)
This fraction is in simplest form because the greatest common divisor of 15 and 8 is 1. As a decimal, \(\dfrac{15}{8} = 1.875\).
Write the x-intercept as a point
The x-intercept is the point with coordinates \(\left(\dfrac{15}{8},\,0\right)\).
Quick check
Substitute \(x=\dfrac{15}{8}\) and \(y=0\) into the original equation:

\(8\cdot\dfrac{15}{8} + 14\cdot 0 = 15 + 0 = 15\)
The equation holds, confirming the result.

See full solution

Graph

Conquer Every Homework with Edubrain

Homework AI Free

FAQs

What is the x-intercept of the line \(8x+14y=15\)?

Set \(y=0\) and solve \(8x=15\). So \(x=\frac{15}{8}\) and the x-intercept is \(\left(\frac{15}{8},0\right)\).

Why do we set \(y=0\) to find the x-intercept?

The x-intercept is the point where the graph crosses the x-axis, and every point on the x-axis has \(y=0\). Solving the equation with \(y=0\) yields the x-coordinate.

What is the y-intercept of the same line?

Set \(x=0\): \(14y = 15\) so \(y = \frac{15}{14}\). The y-intercept is \(\left(0, \frac{15}{14}\right)\).

What is the slope of the line \(8x+14y=15\)?

Rearranged: \(y = -\frac{4}{7}x + \frac{15}{14}\). The slope is \(-\frac{4}{7}\).

How can I graph this line quickly?

Plot the intercepts \(\left(\frac{15}{8}, 0\right)\) and \(\left(0, \frac{15}{14}\right)\), then draw the straight line through them. Two points determine a line.

What is the x-intercept as a decimal?

What if the coefficients were simpler; can I scale the equation?

Yes: multiplying or dividing both sides by a nonzero constant yields an equivalent line. For instance, dividing \(8x+14y=15\) by 2 gives \(4x+7y=\frac{15}{2}\), still same intercepts.

Set y to zero and solve for x now!!
Use our three quick tools below.

185,791+ happy customers
Math, Calculus, Geometry, etc.

Domain and Range Graph Calculator Math AI Solver Calculus Solver