What is the equation of the line??

Answers:

m = -2/3

b = 1

equation:  y = (-2/3)x + 1

This is the same as writing

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Explanation:

There are a few approaches, but I like to start at the y intercept whenever it is an integer. The y intercept is where the diagonal line crosses the vertical y axis. In this case, that location is (0,1) telling us that b = 1 is the y intercept.

From that starting anchor point, we need to find a way to get to another point on this line. There are a few ways to do this, but we can move down 2 and to the right 3 units to go from (0,1) to (3,-1). This "down 2 right 3" motion directly leads to the slope of rise/run = -2/3

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Alternatively, you can start at something like (-3,3) and move down 4 and move right 6 to arrive at (3,-1). Note how rise/run = -4/6 = -2/3. No matter where you start, moving along this line will involve a "down 2 right 3" movement pattern. Be sure to reduce any fractions as much as possible.

Yet another alternative is to apply the slope formula using any two points on the line. Preferably they have integer coordinates.

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However you determine the slope, it's m = -2/3 after fully reducing. It along with b = 1 is plugged into y = mx+b to get y = (-2/3)x+1 as the equation of this line. It's in slope intercept form.

8x + 6y = 28
9x + 3y = 39

to first solve the system, we need to isolate one variable. we will solve for x first so we need to cancel out the y. to do this, we will multiply the second equation by -3

8x + 6y = 28
(9x + 3y = 39) -2

8x + 6y = 28
-18x -6y = -78

now combine

-10x = -50

divide by -10

x=5

now we plug x back into the equation to solve for y

8(5)+6y = 28

40 + 6y = 28

6y= -12

y= -2