Question

find the equation of the linear function represented by the table below in slope - intercept form.

Explanation:

Step1: Calculate the slope

The slope $m$ of a line is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(1,7)$ and $(x_2,y_2)=(2,9)$. Then $m=\frac{9 - 7}{2 - 1}=\frac{2}{1}=2$.

Step2: Find the y - intercept

The slope - intercept form of a line is $y=mx + b$. Substitute $m = 2$, $x = 1$ and $y = 7$ into the equation: $7=2\times1 + b$. Solving for $b$, we get $b=7 - 2=5$.

Step3: Write the equation

The equation of the line in slope - intercept form is $y=mx + b$. Substituting $m = 2$ and $b = 5$, we have $y = 2x+5$.

Answer:

$y = 2x + 5$