Mathematics, 31.01.2020 04:51 jocelynmarquillo1

What is the x-intercept of the line containing the points (–6, 10) and (12, –2)?

Answers: 3

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Answers

Well we have to know the equation of slope > slope(m) = (y2 - y1) / (x2 - x1)
(-6,10) > find our which is the x coordinate in the first set of coordiantes >x1 = -6 and our y which is the first y or our first y int in our first set of coordinates > y1 = 10
(12,-2) Same concept as the first set of coordinates, we are just find the second values now. >x2 = 12 > y2 = -2
Now we have to begin substituting!
slope(m) = $\frac{-2 - 10}{12 - (-6)}$
slope(m) = $\frac{-12}{(12 + 6)}$
slope(m) = $\frac{12}{18}$ < We want to dwindle this as low as possible to get our slope!
slope(m) = $\frac{-2}{3}$
Moving on we have to use y = mx + b now so we know slope(m) = -2/3 which leads us to choose any of your points however I will choose our first set (-6, 10) > x = -6 and y = 10
10 = $\frac{-2}{3}(-6) + b$
10 = 4 + b
10 - 4 = b
6 = b
Now we know that our equation is >y = $\frac{-2}{3x}+ 6$
Let us find the x-intercept by subbing 0 in for y!
y = $\frac{-2}{3x} + 6 \ \textgreater \ 0 = \frac{-2}{3x} + 6 \ \textgreater \ x = 6/ \frac{2}{3} \ \textgreater \ x = 6 * \frac{3}{2} \ \textgreater \ x = \frac{18}{2}$
So just reduce the fraction and we get x = 9! This means our x-intercept is (9, 0)

Answer from: SupremeNerdx

The x-intercept is the point (9,0)

Step-by-step explanation:

we have

$A(-6,10)\ B(12,-2)$

Step 1

Find the slope of the line AB

The formula to calculate the slope is equal to

$m=\frac{y2-y1}{x2-x1}$

Substitute the values

$m=\frac{-2-10}{12+6}$

$m=\frac{-12}{18}$

$m=-\frac{2}{3}$

Step 2

Fin the equation of the line

The equation of the line in point slope form is equal to

y-y1=m(x-x1)

we have

$m=-\frac{2}{3}$

A(-6,10)

Substitute

$y-10=-\frac{2}{3}(x+6)$

$y=-\frac{2}{3}x-4+10$

$y=-\frac{2}{3}x+6$

Step 3

Find the x-intercept

we know that

The x-intercept is the value of x when the value of y is equal to zero

For y=0

Find the value of x

$0=-\frac{2}{3}x+6$

$\frac{2}{3}x=6$

x=9

The x-intercept is the point (9,0)

Answer from: Quest

i you goofed up when writing this, because hnot is not a word minusf is not either. i cannot answer because of that.

step-by-step explanation:

Answer from: Quest

Hello!

the answer is:

the correct option:

b. $x=2.23$

why?

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

$7^{x}=77$

then, using placing logarith with base 7 on both sides of the equation, we have:

$7^{x}=77log_{7}(7^{x})=log_{7}(77)x=log_{7}(77)x=2.2322$

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

$x=2.23$

hence, we have that the correct option:

b. $x=2.23$

have a nice day!

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