Question

What is the equation in slope-intercept form of the linear function represented by the table?

Answer 1

Answer:

$y=2x-6$

Step-by-step explanation:

The equation of a line in slope-intercept form is $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept.

From the table, consider the last two points:

$(4,2)\textrm{ and }(9,12)$

The equation of the line using two points is given as:

$y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1})$

Here, $(x_{1},y_{1})=(4,2)\textrm{ and }(x_{2},y_{2})=(9,12)$

$y-2=\frac{12-2}{9-4}(x-4)\\ y-2=\frac{10}{5}(x-4)\\y-2=2(x-4)\\y-2=2x-8\\y=2x-8+2\\y=2x-6$

Therefore, the equation of the line in slope-intercept form is:

$y=2x-6$