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mojhsa [17]
3 years ago
10

Please help. if a line falls on the points (6,8) and (1,5) what is it’s slope?

Mathematics
1 answer:
Ksenya-84 [330]3 years ago
4 0

Answer:

m= 3/5.

Step-by-step explanation:

The general equation of the line is:

(y - y0) = m ( x - x0), where "m" represents the slope is: (y1 - y0) / (x1 - x0).

From the statement we know that (x1, y1) = (6, 8) and (x0, y0) = (1,5)

Then the slope is:

m= (y1 - y0) / (x1 - x0) = (8 - 5)/(6 - 1) = 3/5.

The slope is 3/5

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We shall begin by expanding the parenthesis on the left side, after which we would combine all terms on and move all of them to the left side, which shall yield a quadratic equation. Then we shall solve.

Let us begin by expanding the parenthesis;

\begin{gathered} (3x-5)^2\Rightarrow(3x-5)(3x-5) \\ (3x-5)(3x-5)=9x^2-15x-15x+25 \\ (3x-5)^2=9x^2-30x+25 \end{gathered}

Now that we have expanded the left side of the equation, we would have;

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\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{Where;} \\ a=9,b=-30,c=150 \\ x=\frac{-(-30)\pm\sqrt[]{(-30)^2-4(9)(150)}}{2(9)} \\ x=\frac{30\pm\sqrt[]{900-5400}}{18} \\ x=\frac{30\pm\sqrt[]{-4500}}{18} \\ x=\frac{30\pm\sqrt[]{-900\times5}}{18} \\ x=\frac{30\pm\sqrt[]{-900}\times\sqrt[]{5}}{18} \\ x=\frac{30\pm30i\sqrt[]{5}}{18} \\ \text{Therefore;} \\ x=\frac{30+30i\sqrt[]{5}}{18},x=\frac{30-30i\sqrt[]{5}}{18} \\ \text{Divide all through by 6, and we'll have;} \\ x=\frac{5+5i\sqrt[]{5}}{3},x=\frac{5-5i\sqrt[]{5}}{3} \end{gathered}

ANSWER:

x=\frac{5+5i\sqrt[]{5}}{3},x=\frac{5-5i\sqrt[]{5}}{3}

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