Question

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

x	0	1	2	3	4
y	5	7	9	11	13

find the slope and y-intercept of the functions graph, and find the equation for the fu
slope:

y-intercept:

equation:

Explanation:

Step1: Calculate the slope

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take the points \((0, 5)\) and \((1, 7)\). Then \( m=\frac{7 - 5}{1 - 0}=\frac{2}{1} = 2 \).

Step2: Find the y - intercept

The y - intercept is the value of \( y \) when \( x = 0 \). From the table, when \( x = 0 \), \( y = 5 \), so the y - intercept \( b = 5 \).

Step3: Write the equation of the line

The equation of a linear function is in the form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Substituting \( m = 2 \) and \( b = 5 \), we get \( y = 2x+5 \).

Answer:

slope: \( 2 \)
y - intercept: \( 5 \)
equation: \( y = 2x + 5 \)