Graph the direct variation y=−1.5x. Using the graph, find:
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The value of x when y=−3; 4.5; 6
Graph the direct variation y=−1.5x. Using the graph, find: The value of x when y=−3; 4.5; 6
To graph the direct variation y = -1.5x, we can start by plotting a few points. Direct variation means that as x increases or decreases, y will also increase or decrease by a constant ratio.
Let's find the values of y when x is -3, 4.5, and 6:
When x = -3, we can substitute this value into the equation to find y:
y = -1.5(-3)
y = 4.5
So when x = -3, y = 4.5.
When x = 4.5:
y = -1.5(4.5)
y = -6.75
So when x = 4.5, y = -6.75.
When x = 6:
y = -1.5(6)
y = -9
So when x = 6, y = -9.
Now, let's plot these points on a graph and draw a straight line connecting them:
-3, 4.5
4.5, -6.75
6, -9
The graph of y = -1.5x will look like a straight line passing through these points.
To graph the direct variation equation y=-1.5x, we can start by choosing some values for x and then calculating the corresponding values for y. The equation indicates that as x changes, y changes in a direct proportion to x with a constant of -1.5 (meaning that for every 1 unit change in x, y changes by -1.5 units).
Let's choose x values of -2, 0, and 2 for simplicity. Note that you can choose any values you want to accurately graph the equation.
Substituting these x values into the equation, we can calculate the corresponding y values:
For x = -2:
y = -1.5(-2) = 3
For x = 0:
y = -1.5(0) = 0
For x = 2:
y = -1.5(2) = -3
Now, we can plot these points (-2, 3), (0, 0), and (2, -3) on a graph. Draw a straight line passing through these points since the equation represents a direct variation, which is a straight line.
To find the values of x when y = -3, 4.5, and 6, we need to identify the corresponding x values on the graph.
- For y = -3, we can see that it intersects the line at x = 2.
- For y = 4.5, it doesn't intersect the line (since the line goes through the points (-2, 3), (0, 0), and (2, -3)), resulting in no real solution for x.
- For y = 6, it also doesn't intersect the line, so there's no real solution for x.
In summary:
- For y = -3, x = 2 (the point (2, -3) on the graph).
- For y = 4.5 and y = 6, there are no real solutions on the graph.
y= mx + b
there is no b so b = 0
You will start your graph at (0,0)
m = -1.5 means that the graph will slant downward from left to right
-1.5 = -3/2 or 3/-2
you can move down -3 and to the right 2
or up 3 and to the left 2 to start your graph. Follow this pattern.
x has to = 2 when y = -3.
dived the y values given by -1.5 to find the other x values.