Mathematics, 12.02.2022 14:00 hellicuh

The equation of line p is y=−4x+1. Line q is perpendicular to line p and passes through (−4, 1). What is the equation of line q? Write the equation in slope-intercept form with no spaces. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

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Answer from: amandaestevez030

$\displaystyle y = \frac{1}{4}\, x + 2$ .

Step-by-step explanation:

The question is asking for the slope-intercept equation of a line. The slope-intercept form equation of a line is in the form $y = m\, x + b$ , where:

(a constant) is the slope of the line, and

(also a constant) is the

-intercept of that line.

For example, the equation of the first line, $y = -4\, x + 1$ , is given in slope-intercept form. The slope of that line is $m_{1} = (-4)$ while the -intercept of that line is $b_{1} = 1$ .

Both and need to be found for the second line.

Start by finding the slope $m_{2}$ of the second line.

Make use of the fact that if two lines in a plane are perpendicular to one another, the product of their slopes would be (-1) . In other words, if a line with slope $m_{1}$ is perpendicular to a line with slope $m_{2}$ , then $m_{1}\, m_{2} = (-1)$ . Rearrange to obtain $m_{2} = (-1) / m_{1}$ .

In this question, since the slope of the first line is $m_{1} = (-4)$ , the slope of the second line (perpendicular to the first line) would be $m_{2} = (-1) / (-4) = (1/4)$ .

Thus, the equation of the second line would be of the form $\displaystyle y = (1/4)\, x + b_{2}$ for some constant $b_{2}$ that needs to be found.

Make use of the fact that the second line goes through the point $(-4,\, 1)$ to find the value of $b_{2}$ . Since the point $(-4,\, 1)\!$ is on the second line, the equation of the second line should hold after substituting in x = (-4) and y = 1 . That is:

$1 = (1/4)\times (-4) + b_{2}$ .

Solve this equation for $b_{2}$ :

$b_{2} = 2$ .

Therefore, the equation of the second line would be $y = (1/4)\, x + 2$ .

Answer from: Quest

whole numbers.

step-by-step explanation:

we are given the average monthly rainfall (in millimeters) model r(m) for the years 1900-2009 as a function of the month number m.

as we can see m is taken for the number of months for years 1900-2009.

we know that number of months can't be a negative number or decimal number or a fraction.

so, the number of months could be only positive whole numbers.

therefore, whole numbers is more appropriate for the domain of r.

Answer from: Quest

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.

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The equation of line p is y=−4x+1. Line q is perpendicular to line p and passes through (−4, 1). Wha...

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