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3 years ago

Write the equation of line in slope-intercept form. Line parallel to y=−2x+3 that passes through the point (−100,−100)

Mathematics

2 answers:

Tems11 [23]3 years ago

4 0

The line with equation y = -2x + 3 has a slope of -2

The line parallel to line with equation y = -2x + 3 has a slope of -2

This is because parallel lines have the same slope

Taking a point (x,y) along the parallel line passing through (-100,-100)

Slope = change in y-axis divide by change in x-axis

-2 = (y - -100) ÷ (x - -100)

-2(x + 100) = y + 100

y = -2x - 300

GrogVix [38]3 years ago

3 0

Remark

The line you want is parallel to y = - 2x + 3

That means it has the same slope as the given line. The given line has a slope of -2

y = -2x + b is what you have so far. Now you have to use the point to get b

y = - 100

x = - 100

Solve for b

-100 = -2(-100) + b

-100 = 200 + b Notice the sign change. Two minus's make a plus. Subtract 200 from both sides.

- 100 - 200 = b

- 300 = b

Answer

y = - 2x - 100

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Find the dot product of the position vectors whose terminal points are (14, 9) and (3, 6).

erma4kov [3.2K]

Answer:

Step-by-step explanation:

The formula for the dot product of vectors is

u·v = |u||v|cosθ

where |u| and |v| are the magnitudes (lengths) of the vectors. The formula for that is the same as Pythagorean's Theorem.

$|u|=\sqrt{14^2+9^2}$ which is $\sqrt{277}$

$|v|=\sqrt{3^2+6^2}$ which is $\sqrt{45}$

I am assuming by looking at the above that you can determine where the numbers under the square root signs came from. It's pretty apparent.

We also need the angle, which of course has its own formula.

$cos\theta=\frac{uv}{|u||v|}$ where uv has ITS own formula:

uv = (14 * 3) + (9 * 6) which is taking the numbers in the i positions in the first set of parenthesis and adding their product to the product of the numbers in the j positions.

uv = 96.

To get the denominator, multiply the lengths of the vectors together. Then take the inverse cosine of the whole mess:

$cos^{-1}\theta=\frac{96}{111.64676}$ which returns an angle measure of 30.7. Plugging that all into the dot product formula: