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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?

Respuesta :

calculista

Answer:

Part 1) [tex]m=2[/tex]

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

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{-2+8}{1+2}[/tex]

[tex]m=\frac{6}{3}[/tex]

[tex]m=2[/tex]

Part 2) What is the y-intercept?

Find the equation of the line in slope intercept form

[tex]y=mx+b[/tex]

we have

[tex]m=2[/tex]

[tex]point\ (1,-2)[/tex]

substitute and solve for b

[tex]-2=2(1)+b\\b=-4[/tex]

so

[tex]y=2x-4[/tex]

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

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

we have

[tex]y=-x+2[/tex] ----> equation A

[tex]y=2x-4[/tex] ----> 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

Ver imagen calculista
aksnkj

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  [tex]y = -x + 2[/tex].

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,

[tex]m=\dfrac{-2-(-8)}{1-(-2)}\\m=\dfrac{6}{3}=2[/tex]

So, the slope of the line is 2.

Now, the equation of the line will be,

[tex]y-(-8)=2(x-(-2))\\y+8=2x+4\\y=2x-4[/tex]

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).

For more details, refer to the link:

https://brainly.com/question/15099560

Ver imagen aksnkj

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