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3 years ago

Determine the intercepts of the line that passes through the following points (1,2) (3,10) (5,18)

Mathematics

1 answer:

musickatia [10]3 years ago

3 0

Answer:

(1/2, 0), (0, -2)

Step-by-step explanation:

We can determine the slope from ...

slope = (change in y)/(change in x) = (10 -2)/(3 -1) = 8/2 = 4

Then an equation for the line can be written for slope m and point (h, k) as ...

m(x -h) -(y -k) = 0

Using the slope we calculated and the first point, we have the equation ...

4(x -1) -(y -2) = 0

4x -4 -y +2 = 0 . . . . . eliminate parentheses

4x -y = 2 . . . . . . . . . . put in standard form

Now, we can divide by the constant on the right to put this into intercept form:

x/(x-intercept) + y/(y-intercept) = 1

x/(1/2) + y/(-2) = 1

The x-intercept is 1/2; the y-intercept is -2.

You might be interested in

How to graph y=-3x+15

steposvetlana [31]

Answer:

Well first you put the y-intercept on the graph. In this case it would be 15

So graph the point (0,15)

The you do the slope which is 3

so you always do rise over run for slope.

If 3 were a fraction it would be 3/1 so go up 3 points and the go right 1 point from (0,15)

hope this helps .-.

3 0

3 years ago

The graph of the equation below is a circle. What is the length of the radius of the circle? (x - 4)^2 + (y + 12)^2 = 17^2

djverab [1.8K]

The correct answer is: [D]: "17" .
______________________________________________________
The radius is: " 17" .
______________________________________________________
Note:
______________________________________________________
The formula/equation for the graph of a circle is:
______________________________________________________
(x − h)² + (y − k)² = r² ;

in which:

" (h, k) " ; are the coordinate of the point of the center of the circle;

"r" is the length of the "radius" ; for which we want to determine;
_______________________________________________________
We are given the following equation of the graph of a particular circle:
_______________________________________________________

→ (x − 4)² + (y + 12)² = 17² ;

which is in the correct form:

→ " (x − h)² + (y − k)² = r² " ;

in which: " h = 4 " ;

" k = -12" ;

"r = 17 " ; which is the "radius" ; which is our answer.

→ { Note that: "k = NEGATIVE 12" } ;

→ Since the equation for this particular circle contains the expression: _________________________________________________________
→ "...(y + k)² ..." ;

[as opposed to the standard form: "...(y − k)² ..." ] ;
_________________________________________________________
→ And since the coordinates of the center of a circle are represented by:
" (h, k) " ;

→ which are: " (4, -12) " ; (for this particular circle) ;
_________________________________________________________
→ And since: " k = -12 " ; (for this particular circle) ;
_________________________________________________________
then:

" [y − k ] ² = [ y − (k) ] ² = " [ y − (-12) ] ² " ;

= " ( y + 12)² " ;

{NOTE: Since: "subtracting a negative" is the same as "adding a positive" ;

→ So; " [ y − (-12 ] " = " [ y + (⁺ 12) ] " = " (y + 12) "
___________________________________________________
Note: The above explanation is relevant to confirm that the equation is, in fact, in "proper form"; to ensure that the: radius, "r" ; is: "17" .
___________________________________________________
→ Since: "r = 17 " ;

→ The radius is: " 17 " ;

which is: Answer choice: [D]: "17" .
___________________________________________________

8 0

3 years ago

Read 2 more answers

Susan's elevation at the top of a mountain is 1,530 meters. After 4 hours of climbing down her elevation is 680 meters. What is

Nitella [24]

Answer:

C) -212.5

Step-by-step explanation:

I've done this question on a quiz before.

Hope I helped!! :D

4 0

3 years ago

The GRE is an entrance exam that most students are required to take upon entering graduate school. In 2014, the combined scores

Ede4ka [16]

$\mathbb P(286$
$\mathbb P(286$

The empirical rule says that approximately 68% of any normal distributed data set lies within one standard deviation of the mean.

$\mathbb P(-2$
$\implies\mathbb P(-2$

The same rule states that about 95% lies within two standard deviations of the mean. Using this rule, and the fact that any normal distribution is symmetric about its mean, you have

$\mathbb P(-2$
$0.95=2\mathbb P(-2$
$\implies\mathbb P(-2$

$\implies\mathbb P(-2$