Question

can u put the two equations in slope intercept form

Answer 1

To answer this question, we need to rewrite both equations in the slope-intercept form of the line. To achieve this, we can proceed as follows:

1. We need to isolate the variable y in both equations. In the first equation, we need to subtract 3x from both sides of the equation:

$3x+2y=2\Rightarrow3x-3x+2y=2-3x\Rightarrow2y=2-3x$

And now, we need to divide both sides by 2 (to isolate the y variable):

$\frac{2y}{2}=\frac{2}{2}-\frac{3x}{2}\Rightarrow y=1-\frac{3}{2}x\Rightarrow y=-\frac{3}{2}x+1$

2. We can proceed in a similar way to find the slope-intercept form of the other line:

$2x-4y=12\Rightarrow2x-2x-4y=12-2x\Rightarrow-4y=12-2x$

Then, we have:

$-\frac{4y}{4}=\frac{12}{4}-\frac{2}{4}x\Rightarrow-y=3-\frac{1}{2}x\Rightarrow y=\frac{1}{2}x-3$

Then, we have both line equations in the slope-intercept form.

Now, to graph both equations, we can use the coordinates of the x- and y-intercepts of both lines:

3. The x-intercept is the point when y = 0. Likewise, the y-intercept is the point when x = 0. We need to evaluate the equation in both cases. Then, we have:

First Line

For y = 0:

$0=-\frac{3}{2}x+1\Rightarrow-1=-\frac{3}{2}x\Rightarrow1=\frac{3}{2}x\Rightarrow\frac{2}{3}\cdot1=\frac{2}{3}\cdot\frac{3}{2}x\Rightarrow\frac{2}{3}=x$

Then, we have the first coordinate: (2/3, 0).

For x = 0:

$y=-\frac{3}{2}x+1\Rightarrow y=-\frac{3}{2}(0)+1\Rightarrow y=1$

Then, the other coordinate for this point is (0, 1)

To graph this line we can use these two points (0, 1) and (2/3, 0).

Second Line

We can proceed in a similar way to find these two coordinates for the second line:

For y = 0:

$y=\frac{1}{2}x-3\Rightarrow0=\frac{1}{2}x-3\Rightarrow3=\frac{1}{2}x\Rightarrow2.3=2\cdot\frac{1}{2}x\Rightarrow6=x\Rightarrow x=6$

The x-intercept is (6, 0).

For x = 0:

$y=\frac{1}{2}x-3\Rightarrow y=\frac{1}{2}\cdot(0)-3\Rightarrow y=-3$

The y-intercept is (0, -3).

To graph this line we can use these two points (0, -3) and (6, 0).

Therefore, the solution for this system of equations is x = 2, y = -2.