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2 years ago

A line goes through the points (4, 5) and (2, -6). Write the equation of the line in point-slope

Mathematics

1 answer:

Lerok [7]2 years ago

5 0

Answer:

m (slope) = $\frac{11}{2}$

Step-by-step explanation:

point-slope form: m= $\frac{y2-y1}{x2-x1}$

(4, 5) (2, -6)

x1 y1 x2 y2

-------------------

$\frac{-6 - 5\\}{2 - 4}$ = m

-6 - 5 = -11

2 - 4 = -2

m = $\frac{11}{2}$

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!!! HELP ME !!!

antoniya [11.8K]

Answer:

DHGB

Step-by-step explanation:

Let's start with 1.

The equation is in standard form (ax+by=c): -4x+2y=8

we'll put it into slope intercept form.

Add 4x onto both sides

2y=4x+8

divide by 2

y=2x+4

Parallel lines have the same slope, but a different y intercept. (the line parallel to this one will have a slope of 2 but a y intercept different from +4)

Looking at the answer choices, the only choice with a slope of 2 is D (y=2x-5)

So the answer to 1 is D

Now 2.

we're given 3 points. One of the points crosses the y axis, which is the y intercept. In this case, the line crosses the point (0,3)

That means the y intercept of the line is (0,3)

here's the line so far:

y=mx+3 (m is a placeholder for the slope)

when given a graph, we can use rise/run. Starting from the point (3,2), we can move 3 spaces to the left, and one up.

In a graph, if you move to the left or downwards, it's a negative move. If you move up or to the right, it's a positive move.

Since we went 1 space up (rise) and 3 spaces to the left, (run) the slope is -1/3

So the line is y=-1/3x+3

Perpendicular lines are negative and reciprocal. If you multiply their slopes, they will equal -1. Their y intercepts don't matter at all.

So to find the slope, we can use this equation.

-1/3m=-1

multiply by -3 on both sides

m=3

Looking at the answer choices, H is the only answer with a slope of 3. So the answer to 2 is H.

Now, 3

You can do the graph method like above for 2, but I'll just calculate the slope.

We're given two points, (-1,-2) and (0,2)

the formula for slope is (y2-y1)/(x2-x1)

we can label the points.

x1=-1

y1=-2

x2=0

y2=2

now, substitute into the equation.

m=(2--2)/(0--1)

m=4/1

the slope is 4.

Now let's use point slope form, which is y-y1=m(x-x1)

once again, sub. into the equation.

y+2=4(x+1)

do distributive prop

y+2=4x+4

subtract by 2

y=4x+2

As said above, parallel lines have the same slope.

Looking at the answer options, G also has the slope of 4

so the answer to 3 is G

Finally, #4

Equation: 3x+y=1

subtract 3x from both sides

y=-3x+1

As said above, perpendicular lines have slopes that multiply to equal -1.

-3m=-1

multiply by -1/3

m=1/3

so the slope of the line will be 1/3.

Looking at the answer options, B also has a slope of 1/3.

So the answer to 4 is B

The code is DHGB

Hope this helps!

4 0

2 years ago

The pipe fitting industry had 546.5 thousand jobs in 2015 and is expected to decline at an average rate of 3 thousand jobs per y

lesya692 [45]

Answer:

The amount of jobs from fitting industry shall decline in 5.5 percent from 2015 to 2025.

Step-by-step explanation:

Due to the assumption of a yearly average rate, a linear function model shall be used. The expected amount of jobs ( $n$ ) after a certain amount of years (t) is given by the following formula:

$n = n_{o} + \frac{\Delta n}{\Delta t}\cdot t$

Where:

$n_{o}$ - Initial amount of jobs in pipe fitting industry, measured in thousands.

$\frac{\Delta n}{\Delta t}$ - Average yearly rate, measured in thousands per year. (A decline is indicated by a negative sign)

If $n_{o} = 546.5$ , $t = 2025-2015 = 10\,years$ and $\frac{\Delta n}{\Delta t} = -3\,\frac{1}{years}$ , then:

$n = 546.5+\left(-3\,\frac{1}{year}\right)\cdot (10\,years)$

$n = 516.5$

The percent change in jobs from pipe fitting industry is calculated as follows:

$\%n = \left(1-\frac{n}{n_{o}}\right)\times 100\,\%$

$\% n = \left(1-\frac{516.5}{546.5}\right)\times 100\,\%$

$\%n = 5.5\,\%$

The amount of jobs from fitting industry shall decline in 5.5 percent from 2015 to 2025.

4 0

2 years ago

A furniture company is ordering screws. The company uses 37 screws to make each table and 14 screws to make each chair. The comp

Firdavs [7]

Answer:

1,400 screws

Step-by-step explanation:

You need 1,1116 screws so 1,400 screws is the right amount.

8 0

2 years ago

Read 2 more answers

The line of reflection will (always, sometimes, never) be the perpendicular bisector between a preimage and it’s reflected image

frez [133]

Answer:

Step-by-step explanation:

line of reflection: a fixed line directly in the middle of the pre-image and the reflected image.

perpendicular: two lines meeting at a 90 degree angle

bisector: line that divides something into two equal parts

pre-image: the original figure before any transformation or translation has been made

reflected image: the original image after being reflected across the line of reflection.

Is the line of reflection a line running perpendicular, directly in the middle of the pre-image and the reflected image? Yes, always would be my answer.

6 0

3 years ago

IDK what to do anymore!!!!

Salsk061 [2.6K]

Answer:

Every morning, I get up and wash my face. Then I sit at my desk and I write. It can be anything. To your future self who will hopefully never read it, a letter to someone you like or don't like regardless of whether you give it to them. Maybe write about what you're feeling in the moments between waking up and sitting down. Don't stop writing until you've emptied your head and put it all on paper.

I don't remember where I learned this but it was called Morning Pages. Some call it Mourning Pages because you're saying goodbye to yesterday and looking forward to the day coming.

Was that what you were looking for??? Or???

3 0

2 years ago