Mathematics, 26.02.2020 08:26 nickthequick

What is the distance between the points (2, 8) and (-6, -7)?

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Answer from: lilly198o

answer:

Step-by-step explanation:Finding the distance, midpoint, slope, equation and the x y-intercepts of a line passing between the two points p1 (2,8) and p2 (-6,-7)

The distance (d) between two points (x1,y1) and (x2,y2) is given by the formula

d = √ ((X2-X1)2+(Y2-Y1)2)

d = √(-6-2)2+(-7-8)2

d = √((-8)2+(-15)2)

d = √(64+225)

d = √289

The distance between the points is 17

The midpoint of two points is given by the formula

Midpoint= ((X1+X2)/2,(Y1+Y2)/2)

Find the x value of the midpoint

Xm=(X1+X2)/2

Xm=(2+-6)/2=-2

Find the Y value of the midpoint

Ym=(Y1+Y2)/2

Ym=(8+-7)/2=0.5

The midpoint is: (-2,0.5)

Graphing the two points, midpoint and distance

P1 (2,8)

P2 (-6,-7)

Midpoint (-2,0.5)

The length of the black line is the distance between the points (17)

Find the slope of the line connecting the two points

Slope = (Y2-Y1) = (-7-8) = (-15) = 1.875

(X2-X1)(-6-2)(-8)

Find the equation of the line passing through the two points

The general equation for a straight line is

y = mx + b

Where m represents the slope of the line which we found in the previous step to be 1.875

y = 1.88x + b

We substitute x and y for the values from one of our points (2,8)

8 = 1.88×2 + b

8 = 3.75 + b

8-3.75 = b

4.25 = b

Knowing both b and m, we can contruct the equation of the line

y= 1.88x+ 4.25

X and Y intercepts

The x-intercept is a point on the graph where y is zero

Using the equation we found in the previous step and substituting zero for y

y= 1.88x+ 4.25

0= 1.88x+ 4.25

-1.88x= 4.25

x= 4.25/-1.88 = -2.27

The x intercept for this straight line is -2.27

The y-intercept is a point on the graph where x is zero

Using the equation we found in the previous step and substituting zero for x

y= 1.88×0+ 4.25

y= 4.25

The y intercept for this straight line is -2.27

Answer from: Quest

function 2 has a greater rate of change than function 1

function 2 has a greater y-intercept than function 1

step-by-step explanation:

$\newline{\text{the rate of change is change per unit time}}$ $\newline{\text{for (x,y), rate of change is }\frac{y_2-y_1}{x_2-x_1} \text{ or change in y divided by change in x}}$ $\newline{\text{for function 1, the cost goes up by 75-45=30 each time every hour}}$ $\newline{\text{that means that the slope of function 1 is 30 per hour}}$ $\newline{\text{for the 2nd function, 40 is added every hour. therefor, the slope is 40 per hour}}$ $\bigskip\newline{\text{since 40 per hour> 30 per hour, function 2 has a greater rate of change than function 1}}$ $\bigskip\newline{\text{the y intercept is the y value when x is 0}}$ $\newline{\text{for function 1, the y value when x is 0 is 45}}$ $\newline{\text{for function 2, the y value when x is 0 (or the flat rate) is 50}}$ $\newline{\text{since 50> 45, function 2 has a greater y intercept than funciton 1}}$ $\bigskip\bigskip\newline{\text{the answers are: }}$ $\newline{\text{ function 2 has a greater rate of change than function 1}}$ $\newline{\text{function 2 has a greater y-intercept than function 1.}}$

Answer from: Quest

sas (side angle side)

aa(angle angle)

sss(side side side)

sas you have to find two sides with an angle in between

aa you find two angles because it will always add up to 180

sss find all sides

step-by-step explanation:

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