Graphing linear equations?! Algebra Help!?

Question

1. y= -2/3x +4 by graphing 3 points.

2. y= x - 3 by graphing 3 points.

3. 3x - 2y = 6 by graphing the x and y intercepts.

4. -x + 3y = -9 by graphing the x and y intercepts.

5. 4x - 3y = 6 by the slope intercept method.

6. 3x + 5y = 12 by the slope intercept method.

Answer 1

Problems 1 and 2 are done by the same method.

Pick any values you want for x, (or for y) and solve the equation for the

other variable.

1. y= -2/3x+4

I pick 3, 6, and -9 for x. You will see why I chose those numbers once

I do the math.

for x=3, y= -2/3(3)+4

y=-2+4, y=2

This gives one point, (3,2)

for x=6, y- -2/3(6)+4

y=-4+4, y=0

This point is (6,0)

for x= -9,y= -2/3(-9)+4

y=6+4, y=10

This point is (-9,10)

I'll do everything I can to avoid fractions!!! Picking x= 3,6, and -9(the

minus sign chosen just for the heck of it) gave me whole numbers for

answers.

Plot these 3 points, draw your line, extended in both directions

beyond the outer points. You're done.

By the way, it takes only two points to draw a straight line.

2. y=x-3

Pretty easy. Pick 0,3, and 5 for example.

y= -3, 0, and 2 for pairs (0,-3),(3,0),(5,2)

3. Here you are going to use only 2 points.

x-intercept is where the line crosses the x-axis. At that point, y has a

value of 0, so the point is found by letting y=0 in the given equation.

3x-2y=6

3x-2(0)=6

3x=6

x=2, and the point is (2,0)

Same deal with the y-intercept. That's where the line crosses the

y-axis, and at that  point x has a value of 0

3x-2y=6

3(0)-2y=6

-2y=6

y= -3, and the point is (0,-3)

Plot those 2 points, and draw your line

4.-x+3y= -9

At x=0, 3y= -9 and y= -3 Point is (0,-3)

At y=0,-x= -9 and x=9. Point is (9,0)

Plot, draw

5.4x-3y=6

Re-arrange to the sope-intercept form y=mx+b

-3y=-4x+6

3y=4x-6

y=(4/3)x-6

The y-intercept occurs at -6units on the y-axis, and the point is

(0,-6)

The slope is 4/3, and it has a positive value. Positive values for slopes

mean the line leans to the RIGHT.

Since slope=rise/run, place your pencil tip at the y-intercept (0,-6)

then "rise" up 4units, then "run" to the right 3 units. That's your

second point. (Point should be (3,-2))

Draw your line

6.3x+5y=12

5y= -3x+12

y=(-3/5)x+12

y-intercept is (0,12)

Slope is  -3/5. Line leans to the LEFT, because it has a negative

value. Starting at (0,12) go DOWN 3 units, then to the Right 5 units

(you should be at (5,9)). Draw your line

Here endeth the Lesson!

Cheers