Round 19.3 to the nearest whole number

Find the equation of the line that passes through (1,3) and is perpendicular to y = 1 − 2 x

egoroff_w [7]

Answer:

$y=\displaystyle\frac{1}{2} x+\displaystyle \frac{5}{2}$

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept.

Perpendicular lines always have slopes that are negative reciprocals (ex. 1/2 and -2, 3/4 and -4/3)

Determine the slope (m):

$y = 1 -2x$

Rearrange into slope-intercept form:

$y = -2x+1$

Now, we can identify clearly that the slope is -2. Because perpendicular lines always have slopes that are negative reciprocals, a perpendicular line would have a slope of $\displaystyle\frac{1}{2}$ . Plug this into $y=mx+b$ :

$y=\displaystyle\frac{1}{2} x+b$

Determine the y-intercept (b):

$y=\displaystyle\frac{1}{2} x+b$

Plug in the given point (1,3) and solve for b:

$3=\displaystyle\frac{1}{2} *1+b\\\\b=\displaystyle \frac{5}{2}$

Therefore, the y-intercept is $\displaystyle \frac{5}{2}$ . Plug this back into $y=\displaystyle\frac{1}{2} x+b$ :

$y=\displaystyle\frac{1}{2} x+\displaystyle \frac{5}{2}$

I hope this helps!

8 0

2 years ago

If y varies directly with x when y=8,x=20 find the value of x when y=42

Alecsey [184]

The value of x is 105 when y=42

Step-by-step explanation:

A direct proportion means that the change in one quantity will also cause the change in other quantity

Given

y varies directly with x

x ∝ y

when the proportionality symbol is removed a proportionality constant is introduced

$x=ky\\k=\frac{x}{y}\\Putting\ y=8\ and\ x=20\\k=\frac{20}{8}\\k = \frac{5}{2}\\So,\ the\ equation\ will\ be\\x=\frac{5}{2}y\\Putting\ y=42\\x=\frac{5}{2}*42\\x=5*21\\x= 105$

The value of x is 105 when y=42

Keywords: Proportion, Direct variation

Learn more about proportion at:

#LearnwithBrainly

5 0

3 years ago

86% percent of senators support a bill. What fraction of senators support the bill?

Natali5045456 [20]

Answer:

$\frac{43}{50}$

Step-by-step explanation:

It was give that 86% percent of senators support a bill.

We want to determine the fraction of senators that supports the bill.

We just have to convert 86% into a fraction in its simplest form.

$86\%=\frac{86}{100}$

$\frac{86}{100}=\frac{2\times43}{2\times50}$

We cancel the common factors to obtain the fraction in the simplest form as:

$\frac{43}{50}$

7 0

3 years ago

Read 2 more answers

SOLVE AND NO LINKS x – 3 = 5

Radda [10]

Answer:

8 = x

or

x = 8

Step-by-step explanation:

x – 3 = 5

x + -3 + 3 = 5 + 3

x = 5 + 3

(5 + 3 = 8)

x = 8

8 0

3 years ago

Read 2 more answers

An object travels along a horizontal straight path at a constant rate. The object travels of the length of the path in second. A

Lelechka [254]

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6 0

3 years ago