Can someone please help me with some math?

Question

I have no idea how to do these math problems. My class is having a test over this so any help would be appreciated. I am horrible at math.

Find the slope-intercept form of the equation of the line described.

1. A line with y-intercept of (0,-5) and x-intercept of (3,0)

2. A line passing through the point (-6,4) and perpendicular to the line passing through the points (7,2) and (-2,8)

Find the value of k so that the given line has the given slope.

3. ( k + 5 ) x + 3y = 21; m = 3/5

Answer 1

http://www.purplemath.com/modules/slopgr...

this website kinda explains how to do it. it's easier to read and understand it than to have someone answer them for you.

Answer 2

1.  y = (5/3)*x - 5

2.  y = (3/2)*x + 13

3.  k = - 34/5

For the first two problems, you need to find an equation in the slope-intercept form:  y = mx + b. "y" and "x" are, of course, not something you need to find which leaves "m" (the slope) and "b" (the y-intercept). Two different things. You are given two points though for the first one which means we can find the slope directly. Once we have the slope, we can pick one of the points and use the point's (x, y) along with the slope (m) to get an equation with only one unknown (b) letting us find the y-intercept. But it gets better. The points actually include the y-intercept so we already know "b" without solving anything! So:

Slope = rise (y) divided by run (x). So if we have two points, we can subtract the second point's values from the first point's values (or the other way around, but we have to do it the same way for both x's and y's!) and have a simple fraction that we can simplify to give us the slope.

1.  (0, -5) and (3, 0)....it doesn't matter that they are intercepts for finding the slope (that only helps us when finding "b")

rise / run = (-5 - 0) / (0 - 3)....do the arithmetic

slope = m = -5 / -3 = 5/3

So far we now have y = (5/3)*x + b. But we were given the y-intercept (which is what "b" is) in the problem. It is -5. Substituting that into the equation we have:

y = (5/3)*x - 5

which is the answer. We can check it by substituting the other point's values and seeing if it works out:

0 = (5/3)*(3) - 5

0 = 5 - 5

0 = 0....checks

2.  For this one you have to remember that perpendicular lines have a special relationship:  their slopes multiply by each other to equal -1. So, if you know the slope of a line perpendicular to the line you need to learn about, you can do a simple bit of algebra to find the slope of the line you need:

slope(1) * slope(2) = -1

But, what is the slope of the other line? Again, use rise/run:

slope(1) = (2 - 8) / [7 - (-2)]

slope(1) = -6 / (7 + 2)

slope(1) = -6/9

slope(1) = -2/3

And back to:

slope(1) * slope(2) = -1....rearrange for slope(2)

slope(2) = (-1) / slope(1)....substitute

slope(2) = (-1) / (-2/3)....change from dividing to multiplying by inverting the divisor (-2/3 --> -3/2)

slope(2) = (-1) * (-3/2)

slope(2) = 3/2

So far you have y = (3/2) * x + b. You know the line passes through the point (-6, 4) so let's use x = -6 and y = 4:

4 = (3/2) * (-6) + b

4 = (-18/2) + b

4 = -9 + b

b = 13

So the equation is: y = (3/2) * x + 13.

3. With this one, we have some equation and must find the value of "k" that makes it work. The wrinkle is that the equation has 2 variables that are not going to help us as they will be in the final equation. So we need something more. And we have it:  m = 3/5. How to use that knowledge? "m" is slope, so if we can arrange the original equation into, say, slope-intercept form, we will know something else about the slope, something else that includes "k" and we can then use that. So:

(k + 5) * x + 3y = 21....subtract (k + 5) * x from each side

3y = - (k + 5) * x + 21....divide each side by 3

y = { - (k + 5) ] / 3} * x + 21/3

So, the two expressions for the slope are:

m = 3/5  and  m = [ - (k + 5) / 3 ]

and we set them equal to each other, then solve for "k":

[ - (k + 5) / 3 ] = 3/5....multiply each side by 15 (15 = 3*5) to get rid of the fractions

[ - (k + 5) ] * 5 = 3 * 3....multiply things out

-5*k - 25 = 9....add 25 to each side

-5*k = 34....divide each side by -5

k = - 34/5

Let's check that:  from just above, we know [ - (k + 5) / 3 ] is supposed to equal 3/5. Does it?

[ - (k + 5) / 3 ] = 3/5....substitute k = =34/5

- (-34/5 + 25/5) / 3 = 3/5....do the addition

- (-9/5) / 3 = 3/5....deal with the two negative signs (-1 * -1 = 1 so they can just be dropped

(9/5) / 3 = 3/5....divide 9/5 by 3

9/15 = 3/5

Which is true (because 3/5 * 3/3 = 9/15).