Questions: Construct a linear function y=mx+b using the date. first find the values of m and b clearly and apply the slopeintercept form. (5) Time (minutes) 10 15 20 25 Flyers 87 112 137 162

Construct a linear function y=mx+b using the date. first find the values of m and b clearly and apply the slopeintercept form.

(5)
Time (minutes) 10 15 20 25
Flyers 87 112 137 162

Transcript text: Construct a linear function $y=m x+b$ using the date. first find the values of $m$ and b clearly and apply the slopeintercept form. \begin{tabular}{|c|c|c|c|c|} \hline (5) \\ \hline Time (minutes) & 10 & 15 & 20 & 25 \\ \hline Flyers & 87 & 112 & 137 & 162 \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Identify the data points

The given data points are:

$ (x_1, y_1) = (10, 87) $
$ (x_2, y_2) = (15, 112) $
$ (x_3, y_3) = (20, 137) $
$ (x_4, y_4) = (25, 162) $

Step 2: Calculate the slope $ m $

The slope $ m $ of a linear function can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the first two points $ (10, 87) $ and $ (15, 112) $: \[ m = \frac{112 - 87}{15 - 10} = \frac{25}{5} = 5 \]

Step 3: Calculate the y-intercept $ b $

The y-intercept $ b $ can be calculated using the slope-intercept form $ y = mx + b $. Rearranging the formula: \[ b = y - mx \] Using the first point $ (10, 87) $ and the slope $ m = 5 $: \[ b = 87 - 5 \times 10 = 87 - 50 = 37 \]

Final Answer

The linear function is: \[ \boxed{y = 5x + 37} \]

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!