Question

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

x	-2	-1	0	1	2
y	-2	1	4	7	10

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

y - intercept:

equation:

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points from the table, say $(0,4)$ and $(1,7)$. Then $m=\frac{7 - 4}{1 - 0}=3$.

Step2: Find the y - intercept

The y - intercept is the value of $y$ when $x = 0$. From the table, when $x=0$, $y = 4$. So the y - intercept $b = 4$.

Step3: Write the equation of the line

The equation of a line in slope - intercept form is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. Substituting $m = 3$ and $b = 4$, we get $y=3x + 4$.

Answer:

slope: $3$
y - intercept: $4$
equation: $y = 3x+4$