A line that passes through the point (5,2) and is parallel to y=x

Mathematics

1 answer:

Molodets [167]3 years ago

8 0

Answer:

y = x - 3

Step-by-step explanation:

Parallel lines have equal slopes.

The line y = x is written in the y = mx + b form, where m = 1, so the slope of the line y = x is 1. The slope of the parallel line is also 1.

The line you want has the form

y = mx + b

The slope is 1, so m = 1, and you get

y = 1x + b

y = x + b

We need to find the value of b.

Replace x and y in the equation with the x- and y-coordinates of the given point, respectively, and solve for b.

y = x + b

2 = 5 + b

b = -3

Now that we know b is -3, we replace b with -3

y = x - 3

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ii) Figure attached

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Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

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$\bar X \pm z_{\alpha/2} \frac{\sigma}{\sqrt{n}}}$ (1)

And for a 90% of confidence the significance is given by $\alpha=1-0.9=0.1$ , and $\frac{\alpha}{2}=0.05$ . Since we know the population standard deviation we can calculate the critical value $z_{0.05}= \pm 1.64$