I'm currently working on a project for algebra in which we have to study two cab companies and their flat fees/how much they charge per mile.
One of the taxi services has a flat fee of $4.25, with an added $0.50 for every mile driven. The question I need answered is "Write an equation in slope-intercept, point-slope, or standard form. Explain why you chose the form you did." I have no clue how to write the equation they are asking me to, or which one to choose. Please help explain this to me! Thank you so much.
pick the one best suited to the problem. You know that you have a rate 0\of .50 for every mile. So, if x is the number of miles, you know you will have something like
y = .5x
But you have a flat fee of 4.25, regardless of the miles, which is tacked on as soon as the meter starts. So,
y = 0.50x + 4.25
In this case, the slope-intercept form is most convenient.
Extra credit: when might the other forms be handier?
Thank you so so much, Steve! It is actually making some sense to me. The point slope would be handier if there was more than one variable, right?
An experiment is underway to test effect of extreme temperature on a newly developed liquid two hours into the experiment the temperature of the liquid is measured to be-17 degrees Celsius after eight hours of the experiment the temperature of the liquid is -47 degrees Celsius assume that the temperature has been changing at a constant rate throughout the experiment and will continue to do so
try using the two-point form of the line. Your two points are (2,-17) and (8,-47)
To write an equation in slope-intercept, point-slope, or standard form, we first need to understand what each form represents.
1. Slope-intercept form: The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope of the line and b represents the y-intercept (the point where the line intersects the y-axis).
2. Point-slope form: The point-slope form of a linear equation is given by y - y₁ = m(x - x₁), where m represents the slope of the line, and (x₁, y₁) represents a point on the line.
3. Standard form: The standard form of a linear equation is given by Ax + By = C, where A, B, and C are constants, and A and B are not both zero. This form generally represents a linear equation without explicitly showing the slope and y-intercept.
Now let's focus on the given problem. We have a taxi service with a flat fee of $4.25 and an additional $0.50 charge for every mile driven. Let's denote the total fare as y and the number of miles driven as x.
To determine which form of the equation to choose, consider what information is explicitly given in the problem. In this case, we are given a flat fee and an additional charge per mile. Since the flat fee represents a constant, we can immediately see that the equation won't be in slope-intercept form since it only represents a straight line with a constant slope. Similarly, the point-slope form may not be the best choice as it represents a line passing through a specific point, which is not explicitly given in our problem.
Therefore, the most suitable form for this problem would be the standard form equation. In this form, we can represent the total fare as follows:
x + (0.50y) = 4.25
Here, x represents the number of miles driven, 0.50y represents the additional charge per mile (since it is $0.50 for every mile), and 4.25 represents the initial flat fee.
Note: If you need to rearrange this equation into slope-intercept form (y = mx + b) or point-slope form (y - y₁ = m(x - x₁)), you can perform algebraic manipulations to isolate y on one side of the equation. But since the problem only asks for an equation, the standard form is sufficient in this case.