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Ulleksa [173]
3 years ago
11

Write down the gradient and y-intercept of each line

Mathematics
2 answers:
Vedmedyk [2.9K]3 years ago
7 0

Answer:

Equation of a line is y = mx + c

where m is the gradient

c is the y intercept

<h2>a.)</h2>

y = 4x - 1

Comparing with y = mx + c

The gradient = 4

y intercept = - 1

<h2>b.)</h2>

y =  \frac{1}{3} x + 3

Comparing with y = mx + c

The gradient is 1/3

The y intercept is 3

Hope this helps you

blondinia [14]3 years ago
7 0

Answer:

4 and  -1

1/3 and 3

Step-by-step explanation:

for y=4x-1

y intercepts where  x=0 so f(0)=4*0-1=-1

y intecepts = -  1

the gradient is y2-y1/x2-x1 where y2=f(x2)=4x2-1 and y1=f(x1)=4x1-1

the gradient is 4x2-1-4x1+1/x2-x1=4 ( the coeficient of x)

for y=1/3x+3

the gradient is 1/3

y intercepts is f(0)=3

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Answer:

z=\frac{0.583 -0.75}{\sqrt{\frac{0.75(1-0.75)}{72}}}=-3.273  

p_v =P(Z  

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Step-by-step explanation:

1) Data given and notation  

n=72 represent the random sample taken

X=42 represent the mechanics who worked on the carcorrectly identified the problem

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p_o=0.75 is the value that we want to test

\alpha represent the significance level

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is less than 0.75:  

Null hypothesis:p\geq 0.75  

Alternative hypothesis:p < 0.75  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.583 -0.75}{\sqrt{\frac{0.75(1-0.75)}{72}}}=-3.273  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

p_v =P(Z  

So the p value obtained was a very low value and using any significance level for example \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of mechanics who worked on the carcorrectly identified the problem is significantly less than 0.75.  

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