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denis23 [38]
2 years ago
12

Question

Mathematics
1 answer:
Goryan [66]2 years ago
8 0

Given:

(2, 4) and (3, 3) are on the line.

To find:

The equation of line in point slope form.

Solution:

If a line passes through a point (x_1,y_1) with slope m, then the point slope form of the line is

y-y_1=m(x-x_1)

(2, 4) and (3, 3) are on the line. So, slope of the line is

m=\dfrac{y_2-y_1}{x_2-x_1}

m=\dfrac{3-4}{3-2}

m=\dfrac{-1}{1}

m=-1

The slope of a line is -1 and it passes through (2,4). So, an equation in point slope form is

y-4=-1(x-2)

Therefore, an equation of the line in point slope form is y-4=-1(x-2).

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Help! ( i'll give brainlisy ) if you don't know the answer then don't type a "answer" and no sending links please.
julsineya [31]

Answer: Linear

The equation is y = 2x-5

Slope = 2

y intercept = -5

====================================================

Explanation:

Each time x goes up by 1, y increases by 2. This directly leads to a linear equation due to the same rate of change no matter where you are in the table.

The slope is rise/run = 2/1 = 2 because "y increases by 2 each time x increases by 1".

We could use the slope formula to see this. Pick on any two rows to plug in the coordinates. I'll use the last two rows

m = (y2-y1)/(x2-x1)

m = (3-1)/(4-3)

m = 2/1

m = 2

This confirms the slope is 2.

The positive slope means that the line goes uphill as you move from left to right.

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

The y intercept is b = -5 because the y intercept always happens when x = 0. This applies to any function, whether it's linear or not.

Together with m = 2 as the slope and b = -5 as the y intercept, we go from y = mx+b to y = 2x-5 as our linear equation

As a way to check, plug in something like x = 1 to find that...

y = 2x-5

y = 2*1-5

y = 2-5

y = -3

The table shows that x = 1 and y = -3 pair up together in the same row, so that confirms x = 1. I'll let you verify the other x values.

3 0
3 years ago
Solve by using square roots. ​ 6x^2−27=39
Bingel [31]

Answer:

Simplifying

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Step-by-step explanation:

Simplifying

6x + -27 = 39

Reorder the terms:

-27 + 6x = 39

Solving

-27 + 6x = 39

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '27' to each side of the equation.

-27 + 27 + 6x = 39 + 27

Combine like terms: -27 + 27 = 0

0 + 6x = 39 + 27

6x = 39 + 27

Combine like terms: 39 + 27 = 66

6x = 66

Divide each side by '6'.

x = 11

Simplifying

x = 11

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Answer:

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