I have four Precalculus problems I need help on :)

[kristenf]

I know it says to show any work I have completed but honestly, I do not know where to start.

I am taking my first college Precalculus class. I am weak in math so I am having trouble understanding certain problems on my hw. I need help with these problems. I am beginning to see a tutor on a reg basis next week, but in the meantime, I need help! This are the problems I am having trouble starting.

Here are some of the hw problems:

(1) A new toyota RAV4 costs $21,000. The car's value depreciates linearly to $10,500 in three years time. Write a formula which expresses its value, V, in terms of its age, t, in years.

(2) rewrite 5x-3y+2=0 in y=b+mx form

(3) find formulas for the linear functions:

slope: -4
x intercept: 7

(4) perpendicular? parallel? neither?

y= 4x+3 ; y=13 - 1/4x


If anyone can help that'd be great - thanks sooooooo much!

 

[Loren]

For #1 if you plotted this on the rectangular coordinate system one point would be at (0,21000) and the second point would be at (3, 10500). The horizontal axis would be t and the vertical axis would be V. Now, using the "two points" formula for a linear equation can you come up with the equation?
\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)

\(\displaystyle y-y_1 = m(x-x_1)\)

 

[mmm4444bot]

(2) rewrite 5x-3y+2=0 in y=b+mx form

y = b + mx is more often written as

y = mx + b

This is called the slope-intercept form of a line's equation.

It's called this because the symbol m is the slope and the symbol b is the y-intercept.

For example:

y = -10x - 4

This equation is slope-intercept form. I can see that the slope of this line is -10 and it crosses the y-axis at (0, -4) because m = -10 and b = -4.

YOUR exercise wants you to perform algebraic manipulations to the given equation so that y ends up all by itself on one side of the equal sign. After you do this, the equation will be in the form

y = mx + b.

To be safe, I suppose you should report it as y = b + mx.

Do you know how to solve an equation for y?

Cheers,

~ Mark

 

[mmm4444bot]

(3) find [a formula] for the linear function [described by]:

slope: -4
x intercept: 7

Hello, again:

This question is also asking for an equation in the form y = mx + b.

If you paid attention to my previous post, then you might be able to write the answer now without having to perform any calculations.

If you've learned about functions per se, then the answer to this exercise might better be expressed in the following form, intead.

f(x) = mx + b

Cheers,

~ Mark



My edit: replaced improperly-referenced pronoun with corresponding noun

 

[mmm4444bot]

(4) perpendicular? parallel? neither?

y= 4x+3 ; y=13 - 1/4x

Heh, heh. Guess what?

Both of the equations are in slope-intercept form.

If you examine both, you will see the slope of each line.

If two lines are parallel, then their slopes MUST be identical.

If two lines are perpendicular then their slopes MUST be negative reciprocals of each other.

(In other words, if m is one slope, then the perpendicular slope is -1/m.)

If neither of these cases is true, then the lines are neither parallel nor perpendicular; they are skewed.

What do you think?

~ Mark

 

[Deleted member 4993]

(2) rewrite 5x-3y+2=0 in y=b+mx form

If anyone can help that'd be great - thanks sooooooo much!

You are given a form:

Ax + By + C = 0 (where A, B & C are constants)

and you need to slove for 'y'

So isolate 'y'

By = -C - Ax

Then divide both sides by 'B' - to get 'y' all alone

y = (-C/B) + (-A/B) x

So now you have the equation in the form

y = b + mx

where

b = -C/B

and

m = -A/B