Question

Find the equation of the linear function represented by the table below in slope-intercept form.Answer: ?(Important: Please check the attached photo before answering the question)

Answer 1

The Slope-Intercept form of the equation of the line is:

$y=mx+b$

Where "m" is the slope of the line and "b" is the y-intercept.

The slope can be found with:

$m=\frac{y_2-y_1}{x_2-x_1}$

Choose two points from the table. These could be the points (1,-4) and (4,-19). You can set up that:

$\begin{gathered} y_2=-19 \\ y_1=-4 \\ x_2=4 \\ x_1=1 \end{gathered}$

Substituting values, you get that the slope of this line is:

$m=\frac{-19-(-4)}{4-1}=-5$

You can substitute the slope and the first point into the equation in Slope-Intercept form:

$-4=1(-5)+b$

Solve for "b":

$\begin{gathered} -4+5=b \\ b=1 \end{gathered}$

Therefore, the Equation of this line in Slope-Intercept form is:

$y=-5x+1$