Word problem: When making a phone call using calling card a call lasting 3 minutes costs $1.60. A call lasting 10 minutes costs $4.40. Let y be the cost of making a call lasting x minutes using a calling card. Write a linear equation that relates to the cost of making the call y, to the time x.
40
To write a linear equation relating the cost of making a call y to the time x, we can use the given information about the cost of calls lasting 3 minutes and 10 minutes.
Let's use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
Using the point (3, $1.60), we have x1 = 3 and y1 = $1.60.
Using the point (10, $4.40), we have x2 = 10 and y2 = $4.40.
First, let's find the slope (m) using the formula m = (y2 - y1) / (x2 - x1):
m = ($4.40 - $1.60) / (10 - 3) = $2.80 / 7 = $0.40
Now we can substitute the values of x1, y1, and m into the point-slope form equation:
y - $1.60 = $0.40(x - 3)
Simplifying, we get the linear equation:
y - $1.60 = $0.40x - $1.20
Rearranging the equation, we have:
y = $0.40x - $1.20 + $1.60
Simplifying further, we get the final linear equation:
y = $0.40x + $0.40
Therefore, the linear equation that relates the cost of making a call y to the time x is y = $0.40x + $0.40.
To write a linear equation that relates the cost of making a phone call y, to the time x, we need to find the equation of a straight line that passes through two given points.
First, let's find the slope (m) of the line using the given information. The slope represents the rate of change of the cost per minute.
We are given two points: (3, $1.60) and (10, $4.40).
Using the formula for slope (m):
m = (y2 - y1) / (x2 - x1)
m = ($4.40 - $1.60) / (10 - 3)
m = $2.80 / 7
m = $0.40
Now that we have the slope, we can use the point-slope form of a linear equation to write the equation of the line:
y - y1 = m(x - x1)
Using one of the given points, let's choose (3, $1.60) as (x1, y1):
y - $1.60 = $0.40(x - 3)
Simplifying the equation, we get:
y - $1.60 = $0.40x - $1.20
Finally, we can rewrite the equation in slope-intercept form (y = mx + b) by moving the constant term to the other side:
y = $0.40x - $1.20 + $1.60
Simplifying further, we get the final linear equation:
y = $0.40x + $0.40
So, the linear equation that relates the cost of making a call (y) to the duration of the call (x) is y = $0.40x + $0.40.
You are given two points:
"a call lasting 3 minutes costs $1.60"
the time, x, is 3 min; the cost, y, is $1.60
(3, 1.60)
"a call lasting 10 minutes costs $4.40"
What do you think the point is from here?
After finding the two points, find the linear equation like you would for any other two points.