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2 years ago

Name two points that are not contained in or lying in plain p

Mathematics

1 answer:

Gwar [14]2 years ago

5 0

Answer:

Points W and Z
plane QRS; plane STU

Step-by-step explanation:

a) points not on the plane will be somewhere other than on the shaded area representing plane P. Z and W are two such points.

b) The name can consist of any three points not on the same line. That means names RVX, RSU, TUV are not allowed, but any other combination of these letters, along with the letter Q, can be used. A couple of possible names are ...

QRS, STU

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2 years ago

Find the equation of the line with slope −5 and that contains the point (−9,−5). Write the equation in the form y=mx+b and ident

Elina [12.6K]

Answer & Step-by-step explanation:

Slope-intercept form:

$y=mx+b$

m is the slope and b is the y-intercept. Insert the given slope:

$y=-5x+b$

To find the y-intercept, take the given coordinate point and insert:

$(-9_{x},-5_{y})\\\\-5=-5(-9)+b$

Solve for b:

Simplify multiplication:

$-5=45+b$

Subtract 45 from both sides:

$-50=b\\\\b=-50$

The y-intercept is -50. Insert:

$y=-5x-50$

$m=-5\\b=-50$

Use the slope formula for when you have two points:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}$

The slope is the change in the y-axis over the change in the x-axis, or rise over run. Insert the points:

$(2_{x1},4_{y1})\\(10_{x2},2_{y2})$

$\frac{2-4}{10-2}=\frac{-2}{8}=-\frac{2}{8}=-\frac{1}{4}$

The slope is $-\frac{1}{4}$ . Insert:

$y=-\frac{1}{4}x+b$

Now follow the steps from the last problem to find the y-intercept. Choose a point and insert into the equation:

$(2_{x},4_{y})\\\\4=-\frac{1}{4}(2)+b$

Solve for b:

Simplify multiplication:

$-\frac{1}{4}*\frac{2}{1}=-\frac{2}{4}=-\frac{1}{2}$

Re-insert:

$4=-\frac{1}{2} +b$

Subtract b from both sides:

$4-b=-\frac{1}{2} +b-b\\\\4-b=-\frac{1}{2}$

Subtract 4 from both sides:

$4-4-b=-\frac{1}{2}-4\\\\-b=-\frac{1}{2}-4$

Simplify subtraction:

$-\frac{1}{2}-4=-\frac{1}{2} -\frac{4}{1} =-\frac{1}{2} -\frac{8}{2} \\\\-\frac{1}{2} -\frac{8}{2}=-\frac{9}{2}$

Re-insert:

$-b=-\frac{9}{2}$

Divide both sides by -1 to make the variable positive (can be seen as -1b):

$b=\frac{9}{2}$

The y-intercept is $\frac{9}{2}$ .

Write the equation:

$y=-\frac{1}{4}x+\frac{9}{2}$

:Done

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3 years ago