Questions: A table of values of a linear function is shown below. x 0 1 2 3 y 3 5 7 9 Find the slope and y-intercept of the function's graph. slope: y-intercept:

A table of values of a linear function is shown below.

x 0 1 2 3
y 3 5 7 9

Find the slope and y-intercept of the function's graph.
slope:
y-intercept:

Transcript text: A table of values of a linear function is shown below. \begin{tabular}{|c|c|c|c|c|} \hline$x$ & 0 & 1 & 2 & 3 \\ \hline$y$ & 3 & 5 & 7 & 9 \\ \hline \end{tabular} Find the slope and $y$-intercept of the function's graph. slope: $y$-intercept:

Solution

Solution Steps

Step 1: Identify the slope

The slope $ m $ of a linear function can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] From the table, we can choose any two points. Let's use $ (x_1, y_1) = (0, 3) $ and $ (x_2, y_2) = (1, 5) $: \[ m = \frac{5 - 3}{1 - 0} = \frac{2}{1} = 2 \] Thus, the slope is $ \boxed{2} $.

Step 2: Identify the $ y $-intercept

The $ y $-intercept is the value of $ y $ when $ x = 0 $. From the table, when $ x = 0 $, $ y = 3 $. Thus, the $ y $-intercept is $ \boxed{3} $.