Write an equation for each line in slope-intercept form.
System of Equations:
f(t)=t+57 g(t)=7t+15 Solution of the system: (7,64) Explanation: See solution.
Practice makes perfect
We have been given a graph that shows the cost of a cabin rental over time for two different cabins.
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 (0,57) and (7,64), we will substitute them into the Slope Formula in order to find the slope.
Thus, the slope of this line is 1.
f(t)=1t+ b ⇔ f(t)=t+ b
Next, we will determine the y-intercept. Since the line passes through the point (0, 57), we can immediately determine the y-intercept as 57. Thus, we can write the full equation of the line.
f(t)=t+57
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 (0,15) and (7,64), we will substitute them into the Slope Formula to find the slope.
Thus, the slope for this line is 7.
g(t)=7t+ b
Let's find the y-intercept now. Since the line passes through the point (0, 15), we can immediately determine the y-intercept as 15.
g(t)=7t+ 15
System of Equations
Finally, we have our system of linear equations.
f(t)=t+57 & (I) g(t)=7t+15 & (II)
The points (0,57) and (0,15) indicate the initial cost for each cabin, $57 and $15. The solution of the system is the point of intersection of the lines, (7,64). It represents the rental cost of each cabin for 7 days, which is $64.
