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Harvey rides his bike at an average speed of 12 miles per hour. In other words, he rides 12 miles in 1 hour, 24 miles in 2 hours, and so on. Let h be the number of hours he rides and d be distance traveled. Write the equation for the relationship between distance and time in point-slope form

The perimeter of a square varies directly with the side length. The point-slope form of the equation for this function is y - 4 = 4(x - 1). Write the equation in standard form

Geoff paddles his canoe at an average speed of 3.5 miles per hour. After 5 hours of canoeing, Geoff has traveled 18 miles. Write an equation in the point-slope form to find the total distance y for any number of hours x

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If this OP is not trying to get solutions to three unrelated questions from a homework, who is? –  Did Dec 8 '12 at 20:01
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closed as too localized by Did, Andrew, Amr, Davide Giraudo, Micah Dec 8 '12 at 23:09

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I will not do your work for you. However, it helps to get started by knowing clearly what you need to know and what you need to do to solve problems like this:

In each question, you are asked to represent the relationship between two variables: how one can be expressed as a function of the other, and you need to establish how one changes with respect to the other.

If you're confused about the difference between the various forms (representations) of an equation (of a line), recall that:

  • the point-slope form for the equation of a line is formatted like this: $(y - y_0) = m(x - x_0)$:
    $m$ = slope, $(x_0, y_0)$ is a particular point on the line.

  • the standard form of an equation of a line is: $ax + by = c$.

  • the slope-intercept form for the equation of a line is $y = mx + b$, again, with $m$ being slope, and $b$ represents the "$y$-intercept": the value of $y$ when $x = 0.$

You should become familiar with each form, because depending on the information you are given, one particular form may be needed. (E.g., if you're given a point on a line, and can determine the slope of a line, then point-slope form comes in handy!)

Once you have an equation in one form, then transitioning from one form to another requires some very basic algebra!


To get you started:

  1. What is your slope $m$ here? $\dfrac{\text{(Change in distance)}}{\text{(change in time)}} = m$.

From what you're given:

$\quad 12 = 12\cdot 1$
$\quad 24 = 12 \cdot 2$

continuing...

$\quad 36 = 12 \cdot 3$

$\quad\quad\;\;\vdots$

$\quad \;d = 12 \cdot h$

What does $12$ represent? This equation gives you the relation between $d$: distance traveled, and $h$: hours spent traveling. Now, simply put it in point-slope form, where $d$ is your "y" and $h$ is your "x": what is your starting point $(x_0, y_0)$?


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Is this your homework? At least try to post some of your work if it is. I'm not here to do your homework for you.

Point slope form for an equation uses the following format: $y - y_0 = m(x - x_0)$

Standard form is: $Ax + By = C$

So if you're given an equation in slope-intercept form, $y = mx + b$, and you want to write it in standard form, move both the variables x and y to the left hand side.

Example: Slope intercept form $y = 2x - 6$ would be $2 x - y = 6$ in standard form.

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