Question

the equation of the problem (hint: what is the slope and y-intercept)-6 -24 -3 -12 0 12 3 24

Answer 1

Given the equation of a straight line

$y=mx+c$

m is the slope and c is the intercept on the y axis

From the table in the question, the equation of the line can be obtained using two points form the equation of a straight line

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Pick two points on the table and substitute for the x values and y values

$(-6,-24)\text{ and (3, -12)}$$\begin{gathered} x_1=-6,y_1=-24 \\ x_2=-3,y_2=-12 \end{gathered}$$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-12-(-24)}{-3-(-6)}=\frac{-12+24}{-3+6}=\frac{12}{3}=4 \end{gathered}$$\begin{gathered} y=mx+c \\ -24=4(-6)+c \\ -24=-24+c \\ c=-24+24=0 \end{gathered}$

Hence, the equation of the table is y = 4x