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# finding a slope of line paaing through a point

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find the slope of line passing through the point (3,4) and (8,-3)

Guest Jul 31, 2017
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Before attempting to do this problem, you must understand the slope-intercept form of a line. It is the following:

$$y=mx+b$$

m = slope of the line

b = the y-intercept (the point where it touches the y-axis)

First, we must find the slope. To do this, we must know another formula. This will solve for m.

$$m=\frac{y_2-y_1}{x_2-x_1}$$

Now that we know the formula, let's plug the given coordinates into the formula above to determine the line's slope:

 $$m=\frac{y_2-y_1}{x_2-x_1}$$ Plug in the coordinate given into this formula to find the slope of the line, $$m=\frac{4-(-3)}{3-8}$$ Remember that subtracting a negative is the same as adding a positive. $$m=\frac{4+3}{3-8}$$ Now, simplify the numerator and denominator into its simplest terms. $$m=\frac{7}{-5}=-\frac{7}{5}$$

We have now determined the slope of the line, -7/5. The next step is to figure out the value of b. First, let's look at the equation with the m filled in.

$$y=-\frac{7}{5}x+b$$

Just plug in a coordinate into here and solve for b. It doesn't matter which coordinate you substitute in, either. I'll use the first point, (3,4):

 $$y=-\frac{7}{5}x+b$$ Plug in the coordinate (3,4) into the equation and solve for b. $$4=-\frac{7}{5}*3+b$$ First, let's simplify the right hand side of the equation by doing -7/5*3 $$-\frac{7}{5}*3=\frac{-7}{5}*\frac{3}{1}=\frac{-21}{5}=-\frac{21}{5}$$ Plug this back into the equation we were solving. $$4=-\frac{21}{5}+b$$ Multiply 5 on both sides of the equation to get rid of the pesky fractions. $$20=-21+5b$$ Add 21 to both sides of the equation. $$41=5b$$ Divide by 5 on both sides. $$\frac{41}{5}=b$$

Now that we have both and solved, we can write the equation in slope intercept form.

$$y=mx+b$$

Just replace and with the numbers we calculated for both. Therefore, your final answer is:

$$y=-\frac{5}{7}x+\frac{41}{5}$$

Here, I have supplied a link to an online graphing calculator called Desmos. It shows you that this is indeed the line that passes through both points. Here is the link: https://www.desmos.com/calculator/0tjwjbb3e7

TheXSquaredFactor  Jul 31, 2017

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