Match the equation with its graph
-2/3 x - 1/4y = 1/3
We need to see the graph.
An easy way to make a match is to look for the intercepts and to check the slope.
To make the equation easier to work with, I would multiply through by a -12
8x + 3y = -4
If x = 0 they y = -4/3
If y = 0 then x = -1/2
look for the points
(0, -4/3) and (-1/2, 0)
the slope is negative
To match the equation with its graph, we need to rearrange it into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Let's start by rearranging the given equation:
-2/3x - 1/4y = 1/3
To isolate the y term, we need to get rid of the x term. Multiply every term by -3/2 to simplify the equation:
(-3/2)(-2/3x) + (-3/2)(-1/4y) = (-3/2)(1/3)
This simplifies to:
x/2 + 3/8y = -1/2
Now, subtract x/2 from both sides:
3/8y = -1/2 - x/2
Simplify the right side:
3/8y = (-1 - x)/2
Next, multiply every term by 8/3:
(8/3)(3/8y) = (8/3)(-1 - x)/2
This gives us:
y = (-8 - 8x)/6
Simplifying further:
y = (-4-4x)/3
Now that we have the equation in slope-intercept form, we can identify the slope (m) and y-intercept (b).
Comparing with the equation y = mx + b, we can see that the slope (m) is -4 and the y-intercept (b) is -4/3.
Now we can plot the graph using the slope (-4) and y-intercept (-4/3).
To plot the graph, start by marking the y-intercept at (0, -4/3). Then, use the slope (-4) to find other points on the line.
The slope (-4) can be written as -4/1. From the y-intercept, we can move down 4 units and to the right 1 unit (or up 4 units and to the left 1 unit) to find another point. Connect these two points to draw the line.
Once the line is drawn, you have successfully matched the equation with its graph.