# Thread: need help with equations

1. ## need help with equations

1)Given: ABCD is a parallelogram

A (-4,8) B (5,2) C (3, -3) D (-6, 3)

the equation of CD is 2x + 3y = 3

write an equation of AB.

2) solve the system of equations graphically

(x - 2) exponent 2 + (y + 3) exponenet 2 = 25

x - y = 4

what is this question asking me and how can i graph this?

2. Originally Posted by zelda1850
1)Given: ABCD is a parallelogram

A (-4,8) B (5,2) C (3, -3) D (-6, 3)

the equation of CD is 2x + 3y = 3

write an equation of AB.

2) solve the system of equations graphically

(x - 2) exponent 2 + (y + 3) exponenet 2 = 25

x - y = 4

what is this question asking me and how can i graph this?

Question 1, you can use point slope equation.

Question 2, substitute, like this.

$\displaystyle (x - 2)^2 + (y+3)^2 = 25$

$\displaystyle x - y = 4$

$\displaystyle x = y + 4$

Substitute:

$\displaystyle ((y+4) - 2)^2 + (y+3)^2 = 25$

$\displaystyle (y+2)^2 + (y+3)^2 = 25$

You can solve this out, or simply recognize that this is a 3-4-5 triangle situation and y = 1 will work, also y = -6.

Edit: I didn't notice the word "graphically."

3. Hello! For #1, if you graph the points, you will see that AB is parallel to CD. You are given the equation of CD: change it into slope-intercept form to find the slope. Since AB and CD are parallel, they will have the same slope. You can then use the slope and one of the points (A or B) to find the equation of the line using the point-slope equation.

For #2, you have a circle and a line. Graph the circle and the line to see where they intersect.

Originally Posted by zelda1850
1)Given: ABCD is a parallelogram

A (-4,8) B (5,2) C (3, -3) D (-6, 3)

the equation of CD is 2x + 3y = 3

write an equation of AB.

2) solve the system of equations graphically

(x - 2) exponent 2 + (y + 3) exponenet 2 = 25

x - y = 4

what is this question asking me and how can i graph this?

4. thx for the first question i changed to slope intercept form and got y = 2/3 x + 1 is that correct?

and they will have same slope so is it the same equation for AB? what did you mean by one of the points in A or B

also for the second question how do i solve it with that equation?

5. Originally Posted by zelda1850
thx for the first question i changed to slope intercept form and got y = 2/3 x + 1 is that correct?

and they will have same slope so is it the same equation for AB? what did you mean by one of the points in A or B

also for the second question how do i solve it with that equation?
For #1 - the equation is actually y = -2/3 x + 1. So, the slope is -2/3. Use this slope along with either point A or point B. Do you remember the point-slope equation? y-y1 = m (x-x1). Use point A or point B as (x1, y1) and m = -2/3. Plug in and solve.

For #2 - you are asked to solve graphically, so you need to graph the circle and the line to see where they intersect.

6. oh so for #1 i used point b and i got is y - 2 = -2/3 (x - 5) is that the equation?

but for #2 dont i need to change the equations before i can graph it?

7. ## Parallelogram

Originally Posted by zelda1850
1)Given: ABCD is a parallelogram

A (-4,8) B (5,2) C (3, -3) D (-6, 3)

the equation of CD is 2x + 3y = 3

write an equation of AB.

2) solve the system of equations graphically

(x - 2) exponent 2 + (y + 3) exponenet 2 = 25

x - y = 4

what is this question asking me and how can i graph this?

Hello Zelda.
I suggest that you go back to square 1 because there appears to be a bit of confusion here. Plot the 4 points. It is a parallelogram. Go directly to line AB info on CD is not needed even if correct Slope of AB = -2/3. Use the point slope formula and point B to determine the equation of AB.

The circle equation given id's its center and its radius. Plot the circle and read off the points of intersection with AB.

bjh