How do you find the slope and y intercept and graph 2x+3y=-62x+3y=−6?

2 Answers
Sally
Apr 22, 2015

Answer

Slope: -2/3−23
y-intercept: (0,-2)(0,−2)

Explanation

There are two simple ways to solve this problem:
1) Algebra
2) Graphing
Let's look at both

1) We can turn the question into the slope-intercept y=mx+by=mx+b form. This is helpful because, when a line is in this form, the slope and y-intercept can immediately be seen. In y=mx+by=mx+b, m=m= slope, and b=b= y-intercept value.

We have to solve for yy in
2x+3y=-62x+3y=−6
We need yy alone. Let's first take 2x2x to the other side by subtracting it.
3y=-6-2x3y=−6−2x
Now, we just have to divide by 33 to get the form y=mx+by=mx+b
y=-6/3-2/3x= -2-2/3x= -2/3x-2y=−63−23x=−2−23x=−23x−2

So in y=-2/3x-2=mx+by=−23x−2=mx+b we can see that m=-2/3m=−23 and b=-2b=−2

2) We can also graph this function and observe.

graph{-2/3x-2 [-10, 10, -5, 5]}

As you can see, the line intersects the y-axis at (0,-2)(0,−2). The slope (rise/run) goes up 2 and left 3, hence the slope of -2/3−23

Meave60
Apr 22, 2015

Solve 2x+3y=-62x+3y=−6 for yy.

Subtract 2x2x from both sides.

3y=-2x-63y=−2x−6

Divide both sides by 3.

y=-2/3x-6/3y=−23x−63 =

y=-2/3x-2y=−23x−2

y=-2/3x-2y=−23x−2 is in slope-intercept form, y=mx+by=mx+b. The slope, mm, is -2/3−23 and the y-intercept, bb, is -2−2.

Determine two points on the line.

If x=0, y=-2/3*0-2=0-2=-2x=0,y=−23⋅0−2=0−2=−2
Point = (0,-2)(0,−2)
If x=3, y=-2/cancel(3)*cancel(3)-2=-4
Point = (3,-4)

Plot the points and draw a straight line through the two points.
graph{y=-2/3x-2 [-14.24, 14.23, -7.12, 7.12]}

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