Question
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(a) The y-intercept is \( \left(0, \frac{10}{3}\right) \). (Simplify your answer. Type an ordered pair, using integers or fractions.) (b) The x-intercept is (Simplify your answer. Type an ordered pair, using integers or fractions.)

Ask by Guerrero Garza. in the United States
Feb 03,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

(a) The y-intercept is \( \left(0, \frac{10}{3}\right) \). (b) The x-intercept cannot be determined without the equation of the function.

Solution

To find the x-intercept and y-intercept of a function, we need to understand the definitions: 1. **Y-intercept**: This is the point where the graph of the function crosses the y-axis. It occurs when \( x = 0 \). 2. **X-intercept**: This is the point where the graph of the function crosses the x-axis. It occurs when \( y = 0 \). ### Given Information - The y-intercept is \( \left(0, \frac{10}{3}\right) \). ### (a) Y-Intercept The y-intercept is already provided as \( \left(0, \frac{10}{3}\right) \). ### (b) X-Intercept To find the x-intercept, we need to set \( y = 0 \) in the equation of the function. However, the equation of the function is not provided in the problem statement. If we assume that the function is linear and can be represented in the form \( y = mx + b \), where \( b = \frac{10}{3} \) (the y-intercept), we can find the x-intercept by setting \( y = 0 \): \[ 0 = mx + \frac{10}{3} \] Solving for \( x \): \[ mx = -\frac{10}{3} \] \[ x = -\frac{10}{3m} \] Without the value of \( m \), we cannot determine the exact x-intercept. If you provide the equation of the function, I can calculate the x-intercept for you. Please provide the function or any additional information needed to find the x-intercept.

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Extra Insights

The x-intercept is the point where the graph intersects the x-axis, which occurs when \( y = 0 \). By substituting \( y = 0 \) and solving for \( x \) in the equation of the line, you can find the x-intercept. If the line is represented in the slope-intercept form \( y = mx + b \), you'd set \( 0 = mx + b \) and solve for \( x \). This gives you the x-intercept as \( \left(-\frac{b}{m}, 0\right) \). To put it all together, if your y-intercept is \( \left(0, \frac{10}{3}\right) \), merely plug in the slope and y-intercept to derive the x-intercept through algebra. Once you have \( x \), you can express the result as an ordered pair, and voilà!

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