System of Equations:
f(t)=0.06t+26 g(t)=0.09t+2 Solution of the system: (800,74) Explanation: See solution.
Practice makes perfect
We have been given a graph that shows the cost of a call over time for two different phone carriers.
We can write an equation for each line in slope-intercept form.
y=mt+ b
In this form, m is the slope and b is the y-intercept. We will find the slope of the lines by using the Slope Formula.
m=y_2-y_1/t_2-t_1
In the above formula, (t_1,y_1) and (t_2,y_2) represent two points of the line.
Equation for f(t)
Let's start with y=f(t), where t represents the number of days. Since the line passes through the points (0,26) and (800,74), we will substitute them into the Slope Formula in order to find the slope.
Thus, the slope of this line is 0.06.
f(t)=0.06t+ b
Next, we will determine the y-intercept. Since the line passes through the point (0, 26), we can immediately determine the y-intercept as 26. Thus, we can write the full equation of the line.
f(t)=0.06t+ 26
Equation for g(t)
We will write an equation for y=g(t) in the same way as we did for f(t). Since the line passes through the points (0,2) and (800,74), we will substitute them into the Slope Formula to find the slope.
Thus, the slope for this line is 0.09.
g(t)=0.09t+ b
Let's find the y-intercept now. Since the line passes through the point (0, 2), we can immediately determine the y-intercept as 2.
g(t)=0.09t+ 2
System of Equations
Finally, we have our system of linear equations.
f(t)=0.06t+26 & (I) g(t)=0.09t+2 & (II)
The points (0,26) and (0,2) indicate the initial fee for each carrier, $26 and $ 2. The solution of the system is the point of intersection of the lines, (800,74). It represents the cost of 800 minutes of call time for both carriers, which is $74.
