Question

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

x	0	1	2	3	4
y	-1	1	3	5	7

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

Explanation:

Step1: Find y - intercept

The y - intercept is the y - value when $x = 0$. From the table, when $x = 0$, $y=-1$.

Step2: Calculate the slope

Use the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0, - 1)$ and $(x_2,y_2)=(1,1)$. Then $m=\frac{1-(-1)}{1 - 0}=\frac{2}{1}=2$.

Step3: Find the equation

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. Substituting $m = 2$ and $b=-1$ gives $y = 2x-1$.

Answer:

y - intercept: -1
slope: 2
equation: $y = 2x - 1$