Mathematics, 06.11.2020 02:50 eleonorajacomopdb7bj

Write the equation in slope-intercept form through the point (4, -1) and is perpendicular to the line y = x + 2 and graph

Answers: 2

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Answer from: destineyburger2

The equation in slope-intercept form through the point (4, -1) and is perpendicular to the line y = x + 2 is: y=-x+3

Step-by-step explanation:

Given equation of line is:

y = x+2

Comparing it with the general form of equation of line in slope-intercept form

y = mx+b

The slope of given line is 1 as the co-efficient of x in the equation is 1.

When two lines are perpendicular, the product of their slopes is -1

Let m1 be the slope of new line

Then

$m.m_1 = -1\\1.m_1 = -1\\m_1 = -1$

The equation of new line perpendicular to given line will be:

y = m_1x+b

Putting the value of m1

y = -x+b

To find the value of b, the given point will be put into the equation

So,

$-1 = -(4)+b\\-1 = -4+b\\-1+4 = b\\b = 3$

The final equation of line is: y = -x+3

Hence,

The equation in slope-intercept form through the point (4, -1) and is perpendicular to the line y = x + 2 is:

y = -x+3

Graph:(Attached)

The graph is made using the online graphing tool "Desmos". The red line in the graph represents the line y = x+2 and the blue line represents the line (y=-x+3) perpendicular to given line

Write the equation in slope-intercept form through the point (4, -1) and is perpendicular to the lin

Answer from: Quest

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

$ab^2+ac^2=bc^2$

$ab^2+ac^2=x^2$ )

triangle abd and cba are similar,

$\frac{ab}{bc}=\frac{bd}{ab}$

$ab^2=bc\cdot bd$

$25=bc\cdot bd$ (2)

triangle cad and cba are similar,

$\frac{ac}{bc}=\frac{cd}{ac}$

$ac^2=bc\cdot dc$

$7\times 7=bc\cdot dc$

$49=bc\cdot dc$ )

using (1), (2) and (3), we get

$25+49=x^2$

$74=x^2$

hence proved.

therefore option 2 is correct.

Answer from: Quest

answer: bea's uncle is 25 years old.

step-by-step explanation:

given the equation $3x- 15= 60$ , we can say that the variable "x" represents the age of bea's uncle. then to find his age, we need to solve for "x":

we must add 15 to both sides of the equation:

$3x- 15+(15)= 60+(15)\\3x=75$

now we need to divide both sides of the equation by 3:

$\frac{3x}{3}=\frac{75}{3}\\\\x=25$

therefore, we can conclude that bea's uncle is 25 years old.

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