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# 2.1E: The Rectangular Coordinate Systems and Graphs (Exercises)

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For the following exercises, find the $$x$$ -intercept and the $$y$$ -intercept without graphing.

1. $$4 x-3 y=12$$
2. $$2 y-4=3 x$$

For the following exercises, solve for $$y$$ in terms of $$x$$, putting the equation in slope-intercept form.

3. $$5 x=3 y-12$$
4. $$2 x-5 y=7$$

For the following exercises, find the distance between the two points.

5. (-2,5)(4,-1)
6. (-12,-3)(-1,5)
7. Find the distance between the two points (-71,432) and (511,218) using your calculator, and round your answer to the nearest thousandth.

For the following exercises, find the coordinates of the midpoint of the line segment that joins the two given points.

8. (-1,5) and (4,6)
9. (-13,5) and (17,18)

For the following exercises, construct a table and graph the equation by plotting at least three points.

10. $$y=\frac{1}{2} x+4$$
11. $$4 x-3 y=6$$