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topjm [15]
3 years ago
8

Write the equation in slope-intercept form of the line that has a slope of 2 and contains

Mathematics
1 answer:
mina [271]3 years ago
8 0

Equation in slope-intercept form is y = 2x - 6

Step-by-step explanation:

  • Step 1: Given slope of the line, m = 2. Form an equation y = mx + b

⇒ y = 2x + b ---- (1)

  • Step 2: The line passes through the point (4,2). So it will satisfy the equation. Find b by substituting x = 4 and y = 2.

⇒ 2 = 2 × 4 + b = 8 + b

⇒ b = -6

  • Step 3: Form the slope-intercept equation.

⇒ y = 2x - 6

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Find the x-intercept<br> y = -3x + 12
Romashka-Z-Leto [24]

Answer:

x-intercept= -4

I could be wrong though

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Prove that \displaystyle \frac{\cos \theta}{1 + \sin \theta} = \frac{1 - \sin \theta}{\cos \theta}
Bogdan [553]

Answer:

sin^2(θ)+cos^2(θ)=1

Step-by-step explanation:

We know that the statement above is true because of the Pythagorean identity theorem, which states the aforementioned equation. If you solve the equation for 1 you get the same equation.

To do this first multiply both sides by cos(θ), this gives you (cos^2θ)/1+sinθ = 1-sinθ

Then, multiply both sides by sinθ. This equals cos^θ=1-sin^2θ.

Finally, add sin^2θ to both sides. This equals the final answer of cos^2θ+sin^2θ=1. Which is true.

7 0
2 years ago
Suppose in this semester, our Exam 1 average was about 86 with an SD of about 10. Suppose the correlation between our Exam 1 and
Oduvanchick [21]

Answer:

the slope of the regression equation for predicting our Exam 2 scores from Exam 1 scores is 0.492

And the y-intercept of the regression equation for predicting our Exam 2 scores from Exam 1 is 33.688

Step-by-step explanation:

Given the data in the question;  

mean X" = 86

SD σx = 10

Y" = 76

SD σy = 8.2

r = 0.6

Here, Exam 2 is dependent and Exam 1 is independent.

The Regression equation is

y - Y" = r × σy/σx  ( x - x" )

we substitute

y - 76 = 0.6 × 8.2/10  ( x - 86 )

y  - 76 = 0.492( x - 86 )

y  - 76 = 0.492x - 42.312

y = 0.492x - 42.312 + 76

y = 0.492x + 33.688

Hence, the slope of the regression equation for predicting our Exam 2 scores from Exam 1 scores is 0.492

And the y-intercept of the regression equation for predicting our Exam 2 scores from Exam 1 is 33.688

4 0
3 years ago
Two planes start from los angeles international airport and fly in opposite directions. the second plane starts 1/2 hour after t
mixer [17]
Let x = first plane's speed.  
We have the equation:
 2 hours * x km/h + 1.5 hours * (x+60) km/h = 3135 km. 
 3.5 hours*x km/h + 90 km = 3135km
 3.5hours*x km/h = 3045km 
 x = 870 km/h. 
 The first plane is traveling at 870 km/h, therefore since it is 60 km/h faster, the second plane is traveling at 930 km/h.
6 0
3 years ago
Which is the graph of the function f(x) = x3 – x2 – 17x - 15?
LenKa [72]

Answer with Step-by-step explanation:

We are given that a function

f(x)=x^3-x^2-17x-15

We have to find the graph of the given function.

y-intercept:It is that  value of y where the graph cut the y- axis.

Let

y=f(x)=x^3-x^2-17x-15

Substitute x=0

Then, we get

f(0)=-15

y-intercept of the graph=-15

x- intercept: It is that value of x where the graph cut the x- axis.

Substitute y=0

x^3-x^2-17x-15=0

Substitute x=-1

-1-1+17-15=0

Therefore,x=-1  is a solution of given equation.

(x+1)(x^2-2x-15)=0

(x+1)(x^2-5x+3x-15)=0

(x+1)(x(x-5)+3(x-5))=0

(x+1)(x+3)(x-5)=0

\implies x=-1,-3,5

Hence, the x-intercept are

-3,-1 and 5

7 0
3 years ago
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