Question

First box options are -22-1/21/2second box options are -55-33Third boxes options are -2-112fourth options -2-121

Answer 1

DEFINITIONS AND FORMULAS

The equation of a straight line can be written in the slope-intercept form to be:

$y=mx+b$

where m is the slope and b is the y-intercept.

The formula to calculate the slope is given to be:

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

SOLUTION

Table 1: Two points can be picked from the table as shown below

$\begin{gathered} (x_1,y_1)=(-5,10) \\ (x_2,y_2)=(0,0) \end{gathered}$

Therefore, the slope is calculated to be:

$m=\frac{0-10}{0-(-5)}=-\frac{10}{5}=-2$

The y-intercept is the value on the y-axis when the x-axis is 0. Therefore:

$\begin{gathered} At \\ x=0,y=0 \\ \therefore \\ b=0 \end{gathered}$

Therefore, the equation of the first table is:

$y=-2x$

Table 2: Two points can be picked from the table as shown below

$\begin{gathered} (x_1,y_1)=(-8,-11) \\ (x_2,y_2)=(1,-2) \end{gathered}$

Therefore, the slope is calculated to be:

$m=\frac{-2-(-11)}{1-(-8)}=\frac{-2+11}{1+8}=\frac{11}{11}=1$

Therefore, the equation of the line is:

$y=x+b$

To find the value of b, we need to substitute one of the ordered pairs in the table into the equation and solve for b:

$\begin{gathered} \text{Using} \\ (x,y)=(1,-2) \\ \therefore \\ -2=1+b \\ b=-2-1 \\ b=-3 \end{gathered}$

Therefore, the equation of the second table is:

$y=x-3$

To get the solution to the system of equations, we can plot the graphs of the equations. This is shown below:

The solution to the system is the point where both graphs intersect.

Therefore, the solution to the system is:

$(x,y)=(1,-2)$

ANSWERS

The equation of the first system is:

$y=-2x$

The equation of the second system is:

$y=x-3$

The solution to the system is:

$(1,-2)$