To graph the line with a slope of -1/2 passing through the point (-1, -2), we can use the slope-intercept form of a linear equation, which is y = mx + b. In this form, 'm' represents the slope, and 'b' represents the y-intercept.
First, we can substitute the given point into the equation to find the value of 'b'. The equation becomes -2 = (-1/2)(-1) + b. Simplifying this, we have -2 = 1/2 + b. To isolate 'b', we subtract 1/2 from both sides, resulting in -2 - 1/2 = b. Simplifying further, we get -5/2 = b.
Now that we have the values of 'm' and 'b', we can write the equation of the line as y = (-1/2)x - 5/2.
To graph the line, we plot the given point (-1, -2) and use the slope to find other points on the line. Since the slope is -1/2, we can use the rise over run method to find additional points. For every 2 units we move down vertically (the rise), we move 1 unit to the right horizontally (the run).
Using this method, we can plot a few more points on the line:
(-1, -2)
(0, -2 + (-1/2)(0)) = (0, -2)
(2, -2 + (-1/2)(2)) = (2, -3)
(4, -2 + (-1/2)(4)) = (4, -4)
Now we can plot these points on a coordinate plane:
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Then, we connect the points with a straight line, and this line represents the equation y = (-1/2)x - 5/2.
I hope this helps!