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algebra: intercepts and parallel lines

1. Using the given equation
a) find the intercepts of its graph and
b)use the intercepts to graph the equation
2x+5y=10

2. Find an equation for the line w/given properties Parallel to the line 5x-y=-10; containing the point (0,0)
y=___

3. Find the equation of a line that is perpendicular to the line y=1/9x+9 and contains the point (-3,0), y=____

4. A circle has the equation 2(x-2)^2+2y^2=2
Find the center (h,k) and radius r and graph the circle. Find the intercepts, if any of the graph.
What are the intercepts?
State the center____
State the radius_____

5. Find the center (h,k) and radius r of the circle with the given equation. 4 (x+4)^2+4(y-5)^2=36

6. A circle has the equation 4x^2+4y^2-32x-16y-20=0
Graph the circle using the center (h,k) and radius r.
Find the intercepts, if any, of the graph.

Solution Preview

Please see attached.

a) At ANY x-intercept you know that the y-coordinate MUST BE 0, ALWAYS!. So the x-coordinate of the x-intercept may be found by replacing the "y" in the equation with a 0 and then solving for the value of "x". In this case you get:

Now, by dividing both sides of the last equation by 2 we will know the value that x takes when y = 0: . So, the x-intercept has coordinates, .
A similar strategy will allow you to find the y-intercept. At ANY y-intercept the x coordinate MUST BE 0, ALWAYS! So now we will replace the "x" in the equation with 0 and then solve the resulting equation for the value of "y". Here's what we get:

Now, by dividing both sides of the last equation by 5 we will find the value that y takes when x = 0 : . So, the y-intercept has coordinates, .
b) Plotting the x- and y-intercepts that we just found and then drawing a straight line through them allows us to produce the graph of the equation, . Here is the graph:

2. Find an equation for the line w/given properties Parallel to the line 5x-y=-10; containing the point (0,0)
y=___

If two lines are parallel then you know that their slopes must be equal. The easiest way to find the slope of a linear equation that you're given is to solve it for y. Once you've solved it for y the slope is just whatever number is left multiplying x. If you add y to both sides of the equation, , and ...

Solution Summary

Intercepts and parallel lines in algebra are examined.

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