Mathematics, 19.01.2020 06:31 hannahkharel2

Caleb graphed the linear function y = –x + 2 of a system of equations. the other linear function passes through the points (–2, –8) and (1, –2). what is the slope of the linear function that passes through the points (–2, –8) and (1, –2)? what is the y-intercept? graph the linear function to determine the solution. what is the solution?

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The slope of the line is 2. The y-intercept will be equal to -4 or 4 units (absolute value). The solution of the system of equations will be (2,0).

Given information:

The linear function is y = -x + 2 .

Other linear function passes through the points (–2, –8) and (1, –2).

Now, the slope of the function passing through (–2, –8) and (1, –2) will be,

$m=\dfrac{-2-(-8)}{1-(-2)}\\m=\dfrac{6}{3}=2$

So, the slope of the line is 2.

Now, the equation of the line will be,

$y-(-8)=2(x-(-2))\\y+8=2x+4\\y=2x-4$

From the above equation of the line, the y-intercept will be equal to -4 or 4 units (absolute value).

The graph of the system of lines is attached as an image in the solution.

The point of intersection of the two lines will be the solution of the system. So, the solution will be (2,0).

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Caleb graphed the linear function y = –x + 2 of a system of equations. the other linear function pas

Answer from: jayceerocks5614

Part 1) m=2

Part 2) The y-intercept is the point (0,-4)

Part 3) The solution of the system is (2,0) (the graph in the attached figure)

Step-by-step explanation:

Part 1) What is the slope of the linear function that passes through the points (–2, –8) and (1, –2)?

The formula to calculate the slope between two points is equal to

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

substitute the values

$m=\frac{-2+8}{1+2}$

$m=\frac{6}{3}$

m=2

Part 2) What is the y-intercept?

Find the equation of the line in slope intercept form

y=mx+b

we have

m=2

$point\ (1,-2)$

substitute and solve for b

$-2=2(1)+b\\b=-4$

y=2x-4

The y-intercept is the point (0,-4)

Part 3) Graph the linear function to determine the solution. What is the solution?

we have

y=-x+2 ----> equation A

y=2x-4 ----> equation B

Solve the system by graphing

The solution is the intersection point both graphs

using a graphing tool

The solution of the system is (2,0)

see the attached figure

Answer from: Quest

coins of silver or gold

step-by-step explanation:

Answer from: Quest

solution:

the given function is ,

$f(x) = 4 x^3 - 72 x^2 + 320 x,$

= $4x( x^2- 18 x + 80)\\\\ 4 x(x^2-10 x -8 x + 80) \\\\ 4 x[(x-10)(x-8)]$

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

$f(x) = a x^3+ b x^2 + c x+d,$

sum of the roots = a + b +c= 0+8+10=18= $\frac{-b}{a}$

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 = $\frac{c}{a}$

product of roots = a b c = 0= $\frac{d}{a}$

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function $f(x) = 4 x^3 - 72 x^2 + 320 x,$ is given by entry and exit route of this hall.

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Caleb graphed the linear function y = –x + 2 of a system of equations. the other linear function pas...