a Use the x- and y-intercepts to find the slope and y-intercept of the line.
B
b Perpendicular lines have slopes whose product is -1.
C
c Use the Slope Formula to determine the slope of the line.
D
d The first hour can be viewed as a fixed cost.
A
a y=- 1/2x+4
B
b y=2x-1
C
c y=2/5x+7/5
D
d C=15+7(t-1), t≥1 or C=8+7t, t≥1
Practice makes perfect
a To find the equation of the line, we have to determine it's slope m and y-intercept b.
y=mx+ b
Examining the diagram, we can identify where the line intercepts the y-axis.
The line intercepts the y-axis at (0,4) which means b= 4. To find the slope, we have to measure the vertical and horizontal distance between two points on the graph. Since the x- and y-intercepts of the graph are on the gridlines, we can use these to identify the slope.
Traveling between the y- and x-intercept requires that we move 8 steps horizontally in the positive direction and 4 steps vertically in the negative direction. With this, we can find the slope.
rise/run=- 4/8 ⇔ m= - 1/2
Now that we have the slope and y-intercept, we can write our final equation.
y= mx+b
y= - 1/2x+4
b To write the equation of a line perpendicular to the line and through (-1,-3), we first need to determine the slope. Two lines are perpendicular when their slopes are opposite reciprocals. This means that the product of a given slope and the slope of a line perpendicular to it will be -1.
m_1*m_2=-1
From Part A, we know the slope of the line. By substituting this slope into the equation, we can solve for the slope of the perpendicular line, m_2.
Any line perpendicular to the given line will have a slope of 2 which means we can write the equation in the following form.
y=2x+b
To find b, we substitute the coordinates of (- 1,- 3) in the equation and solve for b.
The equation of the line through (- 1,- 3) that is perpendicular to the given line is y=2x-1.
c As in Parts A-C, we have to find the slope and y-intercept of the line that passes through the given points. When we have two points, we can use the Slope Formula to determine the slope.
d If we assume that 1 hour is the minimum amount of time, the $15 charge can be viewed as a fixed cost for using the parking lot. After the first hour, the charge per hour is $ 7. This will be our slope. Let's write this as an equation.
C=15+7(t-1) where t≥ 1
Notice that if t= 1, we only have to pay the starting fee of $15 as 7( 1-1)=0 When the number of hours goes beyond 1, we pay the additional $ 7 per hour. Also, we could always rewrite the function by distributing 7.
