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# Write an equation of the line that passes through the given points in any form.

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Write an equation of the line that passes through the given points in any form.

X     Y

-1     3.5

1     -.5

3     -4.5

Find the Equation:

Feb 2, 2021

#1
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This question gives more information than necessary because writing the equation of a line really only requires two points. The third one is not really necessary.

Let's find the slope of the line. Since the slope of any line is constant, the two points used to compute the slope is immaterial. Just pick any two. I will pick thw first two in the table, $$(-1,\frac{7}{2})\text{ and } (1,-\frac{1}{2})$$.

$$m=\frac{\frac{7}{2}-(-\frac{1}{2})}{-1-1}\\ m=-\frac{4}{2}\\ m=-2$$

Because we can write the equation in any form, I will opt for point-slope form, as it is probably the easiest one to construct in this particular situation.

Point-slope Form: $$y-y_1=m(x-x_1)$$ where m is the slope and $$(x_1,y_1)$$ is any point on the line.

Equation of Line: $$y-\frac{7}{2}=-2(x+1)$$

Feb 2, 2021

#1
+1

This question gives more information than necessary because writing the equation of a line really only requires two points. The third one is not really necessary.

Let's find the slope of the line. Since the slope of any line is constant, the two points used to compute the slope is immaterial. Just pick any two. I will pick thw first two in the table, $$(-1,\frac{7}{2})\text{ and } (1,-\frac{1}{2})$$.

$$m=\frac{\frac{7}{2}-(-\frac{1}{2})}{-1-1}\\ m=-\frac{4}{2}\\ m=-2$$

Because we can write the equation in any form, I will opt for point-slope form, as it is probably the easiest one to construct in this particular situation.

Point-slope Form: $$y-y_1=m(x-x_1)$$ where m is the slope and $$(x_1,y_1)$$ is any point on the line.

Equation of Line: $$y-\frac{7}{2}=-2(x+1)$$

Guest Feb 2, 2021