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1 year ago

What is the equation of the line that is perpendicular to y = 3x + 3 and passes through the point (−6, 9)?

Mathematics

1 answer:

Ludmilka [50]1 year ago

7 0

The equation of the line will be equal to 3y = -x + 21.

A line may be defined as the straight figure drawn which has no end points. The equation of a line can be written in slope intercept form as y = mx + c where m is the slope of line, c is y intercept an x and y are independent and dependent variables. If a point (x₁, y₁) is given then equation of line is (y - y₁) = m (x - x₁). The slope of line which is perpendicular to a given line having slope m is equal to -1/m.

Now, equation of line is y = 3x + 3. If we compare with slope intercept form then, m = 3. Now, slope of line perpendicular to this line is equal to -1/3. Now, equation of line passing through point (-6, 9) is given as

(y - 9) = -1/3 (x + 6)

3y - 27 = -x - 6

=> 3y = -x + 21 which is the required equation of line.

Learn more about Slope intercept form at:

brainly.com/question/9317111

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klasskru [66]

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As the total cost includes the payment for entering the patch also,

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3 years ago

Laws of Sines with find the angle.

Jobisdone [24]

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3 years ago

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Determine if the table shows a linear or an exponential function

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Answer:

<em>The table shows an exponential function</em>

Step-by-step explanation:

<u>Linear vs Exponential Functions</u>

A linear function is written as:

$y=mx+b$

where m and b are constants.

If a table contains a linear function, then for each pair of ordered pairs (x1,y1) and (x2,y2), the value of m must be constant.

The slope can be calculated as:

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

An exponential function is written as:

$y=y_o.r^x$

Where r is the ratio and yo is a constant.

If a table contains an exponential function, for two ordered pairs (x1,y1) and (x2,y2), the value of r must be constant.

The ratio can be calculated as:

$\displaystyle r=\sqrt[x2-x1]{\frac{y2}{y1}}$

Calculate the slope for (0,4) and (1,2):

$\displaystyle m=\frac{2-4}{1-0}=-2$

Calculate the slope for (1,2) and (2,1):

$\displaystyle m=\frac{1-2}{2-1}=-1$

Since the slope is not the same, the function is not linear.

Now calculate the ratio for (0,4) and (1,2)

$\displaystyle r=\sqrt[1-0]{\frac{1}{2}}$

The radical of index 1 is simply equal to its argument:

$\displaystyle r=\frac{1}{2}$

Now calculate the ratio for (0,4) and (2,1)

$\displaystyle r=\sqrt[2-0]{\frac{1}{4}}$

$\displaystyle r=\sqrt{\frac{1}{4}}$

$\displaystyle r=\frac{1}{2}$

Testing other points we'll find the same ratio, thus the table is an exponential function

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3 years ago

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777dan777 [17]

Answer:

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serious [3.7K]

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