Given the linear equation y=-3/5x-4, find the y-coordinates of the points (-5, ), (0, ), and (5, ). Please show all of your work. Plot those points and graph the linear equation.
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To get the missing "y" value for each point, use the corresponding x value (which is provided) and plug it into the equation y = (-3/5)x - 4
For example, when x = -5,
y = (-3/5)*(-5) -4 = 3 -4 = -1
so the first point is (-5,-1)
Now, you do the other two points and plot the graph. The slope of the line should be -3/5.
To find the y-coordinates of the points (-5, ), (0, ), and (5, ) on the given linear equation y = (-3/5)x - 4, we need to substitute the x-values into the equation and solve for y.
1. Point (-5, ):
Substitute x = -5 into the equation:
y = (-3/5)(-5) - 4
y = 15/5 - 4
y = 3 - 4
y = -1
So, the y-coordinate of point (-5, ) is -1.
2. Point (0, ):
Substitute x = 0 into the equation:
y = (-3/5)(0) - 4
y = 0 - 4
y = -4
So, the y-coordinate of point (0, ) is -4.
3. Point (5, ):
Substitute x = 5 into the equation:
y = (-3/5)(5) - 4
y = -15/5 - 4
y = -3 - 4
y = -7
So, the y-coordinate of point (5, ) is -7.
Now, let's plot these points on a graph:
Point (-5, -1)
Point (0, -4)
Point (5, -7)
To graph the linear equation y = (-3/5)x - 4, we can plot a few more points and draw a straight line through them. Here's one way to do it:
- Choose a few more x-values, such as x = -10, -8, -6, -4, -2, 2, 4, 6, 8, 10.
- Substitute each value of x into the equation, calculate the corresponding y-value, and plot the points.
- Draw a straight line passing through all the plotted points.
For example, substituting x = -10 into the equation:
y = (-3/5)(-10) - 4
y = 30/5 - 4
y = 6 - 4
y = 2
So, another point on the line is (-10, 2). Similarly, you can find more points and plot them.
Once you have enough points plotted, connect them with a straight line. That line represents the graph of the given linear equation.