Im trying to plot 3x-3y= -9 on a grid so how do i solve this and find B if y=mx+b

Question

also how do i find the same x and y intercept of 3x-3y= -9 and this other equation 2x+y=9. Like were is the intercept of both of these and how do i solve to get the intercept?

Answer 1

First, I would divide both sides of the equation by 3 to get

 

x - y = -3

 

Then solving for y,

 

y = x + 3

 

 

The first point is the y-intercept, which is (0, 3).  Then the second point can be found using the slope.  The slope is 1.  Move one to the right, then one unit up to get the point (1, 4).  Keep using the slope and the preceding point to get more points on that line.  The third point is (2, 5).

 

 

To find the y-intercept, set x=0 and solve for y.

To find the x-intercept, set y=0 and solve for x.

 

Note that b is the y-intercept in   y=mx+b.

 

 

To find the points and intercepts, do the same procedure as the first equation.

 

2x + y = 9   becomes    y = -2x + 9

 

 

Answer 2

Hi Brett,

The simplest way to think of intercepts are where x=0 (y-intercept) and y=0 (x-intercept), respectively. 

For 3x - 3y = -9, so for x: 3x - 3y (+3y) = -9 + 3y --> 3x (/3) = (3y-9)/3

--> x = y - 3, so where y=0 is your x-intercept --> x = -3

To put the equation into y = mx + b:

3x - 3y = -9 --> 3x - 3y (-3x) = -9 (-3x) --> -3y = -3x - 9 --> -3y(/-3) = (-3x-9)/-3

--> y = x + 3, so m(slope) = 1 & your b (y-intercept) = 3

 

I hope this helps! Try this method now with the 2nd equation: 2x + y = 9.

Good luck,

Clyde W.

 

Answer 3

To graph any equation/inequality you must express y in terms of x, or to bring to the slope/intercept form: y = mx +b. 

Let's do this for equation: 3x - 3y = -9, let's remove the common factor for all numbers (3), or divide both sides by 3. We get:  x - y = -3. Now isolate y by moving x to the right: -y = -x -3, now let's change all signs to opposite in order to have y positive (must be always), we do that by multiplying both sides by (-1). Now we got nice looking equation:

y = x +3. Lets draw the line. See below. We'll do the same manipulations with the second equation: 2x+y = 9.

Or y = -2x +9.  Intersection of those two lines will give us the solution of the problem. 

 

The answer - intersection point is (2,5), or x = 2, y = 5. Sorry I drew a graph, scanned it and couldn't insert or attach. 

Just draw on graph paper both lines and you will get the solution, intersection point of two graphs. 

 

Sorry, couldn't insert the graph. 

 

Regina G