Find the slope of the line through each pair of point

Mathematics

1 answer:

Rashid [163]3 years ago

4 0

The slope of the line passes through (-6, 3) and (1, 5) is $\frac{2}{7}$

Solution:

Given, two points are (- 6, 3) and (1, 5)

We have to find the slope of a line that passes through the above given two points

Slope of a line that pass through $\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right)$ is given as:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\text { Here, in our problem, } x_{1}=-6, y_{1}=3 \text { and } x_{2}=1, y_{2}=5$

$\text { Slope } m=\frac{5-3}{1-(-6)}=\frac{2}{1+6}=\frac{2}{7}$

Hence, the slope the line that passes through the given points is $\frac{2}{7}$

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By multiplying each component in $\vec r_1$ by 5, we have

$\dfrac{\partial\vec r_2(u,v)}{\partial u}=5\dfrac{\partial\vec r_1(u,v)}{\partial u}$

and the same goes for the derivative with respect to $v$ . Then the area of the surface given by $\vec r_2(u,v)$ is

$\displaystyle\int_{-4}^4\int_{-4}^425\left\|\frac{\partial\vec r_1(u,v)}{\partial u}\times\frac{\partial\vec r_1(u,v)}{\partial v}\right\|\,\mathrm du\,\mathrm dv=\boxed{25}$