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3 years ago

The slope-intercept form of a line is y=mx+b .

Mathematics

1 answer:

d1i1m1o1n [39]3 years ago

3 0

Answer:

$m$ is the slope and $b$ is the y-intercept.

Step-by-step explanation:

The slope-intercept form of a line is given as:

$y=mx+b$

Here, the coefficient of $x$ represents the slope of the line.

The coefficient of $x$ is $m$ and hence the slope.

y-intercept is the value of $y$ for which is $x$ is 0.

Now, if we put $x$ as 0 in the above equation, we get

$y=m(0)+b\\ y=0+b\\ y=b$

Therefore, y-intercept is $b$ .

Hence, for the line with slope-intercept form $y=mx+b$ , $m$ is the slope and $b$ is the y-intercept.

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1) What does the equation x = 4 represent in R^2? a) a circle.b) a plane.c) a line.d) a pointWhat does it represent in R^3? a) a

Sunny_sXe [5.5K]

Answer:

The equation $x=4$ represents in R^2 c) a line

The equation $x=4$ represents in R^3 a) a plane

The equation $y+3x=2$ represents in R^3 a) a plane

The equation $z-4y=8$ represents d) a plane

The pair of equations $y=2,z=8$ represents a) a line

Step-by-step explanation:

Let's start by studying each question :

In R^2 , $x=a$ with $a$ ∈ IR is the equation of all vertical lines

In this case, the only free variable is the variable ''y''

R^2 has two dimensions (x and y) so if we set $x=4$ we will have only one free variable in R^2 (which is a line in R^2). Therefore, $x=4$ represents a line in R^2

Now, in R^3 we have three dimensions (x, y and z) so if we set $x=4$ we will have only two free variables (y and z) and $x=4$ will represent a plane (which have two dimensions) in R^3.

2) The equation $y+3x=2$ in R^3 has the free variable ''z'' and given that we select a value (for example for ''x'') the another value from the variable ''y'' is determined. Finally, we have the free variables ''z'' and ''x'', and the variable ''y'' restricted for our choice of the variable ''x''.

The equation $y+3x=2$ in R^3 (given that we have two free variables) represents a plane.

Using the same reasoning, the equation $z-4y=8$ represents a plane (given that it has two free variables : ''y'' and ''x'')

Finally, the pair of equations $y=2,z=8$ set values for ''y'' and ''z'' leading us ''x'' as the free variable. With only one free variable we will have a ''one dimensional'' geometric form. The one dimensional forms in R^3 are lines.

The final answer is a) a line.

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2 years ago

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erastova [34]

AWNSER: B or 54

Hope this helps and Happy Friday!

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2 years ago

Solve.E6xplain how you get the answer without using a calculator 6/3 + 1/2

fiasKO [112]

I'm just gonna assume that 6/3 and 1/2 are fractions.

First you have to find common denominators for the fractions to be added.

The first common denominator divisible by both the denominators is 6.

So 2x3=6 and 1x3=3

and 3x2+6 and 6x2+12

so that would be 12/6 + 3/6

Then you would proceed to add both of the numerators together which are 12 and 3.

To get a total of 15/6. You can also simplify that into a mixed number 2 1/2.

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3 years ago

Find the co-ordinates of the points where the line represented by the linear equationy = 2x -4 intersects x-axis and y-axis.

nikdorinn [45]

Step-by-step explanation:

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3 years ago

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Alexeev081 [22]

Step-by-step explanation:

6.3%

that is the correct answer

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2 years ago

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