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\begin{tabular}{|l|l|}\hline 14) Evaluate each function for the given input values. \\ For \( f(x)=5 x+1 \), find \( f(x) \) when \( x=2 \) and when \( x=3 \). \\ 16) Write the equation that describes the line in slope- \end{tabular}

Ask by Ortiz Olson. in the United States
Jan 25,2025

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Answer

For \( f(x) = 5x + 1 \): - When \( x = 2 \), \( f(2) = 11 \) - When \( x = 3 \), \( f(3) = 16 \) The equation of the line in slope-intercept form is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Solution

Let's solve the problems step by step. ### Problem 14: Evaluate the function \( f(x) = 5x + 1 \) 1. **Find \( f(2) \)**: \[ f(2) = 5(2) + 1 \] Calculate: \[ f(2) = 10 + 1 = 11 \] 2. **Find \( f(3) \)**: \[ f(3) = 5(3) + 1 \] Calculate: \[ f(3) = 15 + 1 = 16 \] So, the evaluations are: - \( f(2) = 11 \) - \( f(3) = 16 \) ### Problem 16: Write the equation that describes the line in slope-intercept form The slope-intercept form of a line is given by the equation: \[ y = mx + b \] where \( m \) is the slope and \( b \) is the y-intercept. To write the equation, we need the values of \( m \) and \( b \). If you have specific values for the slope and y-intercept, please provide them. Otherwise, I can help you with a general example. For example, if the slope \( m = 2 \) and the y-intercept \( b = 3 \), the equation would be: \[ y = 2x + 3 \] Please provide the slope and y-intercept if you have them, or let me know if you need further assistance!

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Bonus Knowledge

To evaluate the function \( f(x) = 5x + 1 \) for the inputs \( x = 2 \) and \( x = 3 \), simply substitute \( x \) into the equation. For \( x = 2 \), \( f(2) = 5(2) + 1 = 10 + 1 = 11 \). For \( x = 3 \), \( f(3) = 5(3) + 1 = 15 + 1 = 16 \). So, \( f(2) = 11 \) and \( f(3) = 16 \). Now, when writing the equation for a line in slope-intercept form, remember that it follows the format \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. If you want to create an equation, simply determine your slope and where the line crosses the y-axis, and you're ready to go!

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