Question

4.

Which graph represents the following system of equations?

y = 3x + 3
y = –x – 3


A. Graph c


B. Graph b


C. Graph d


D. Graph a

Answer 1

Step-by-step explanation:

Answer:

See picture attached below.

Step-by-step explanation:

To graph the system, graph each line separately.

y = 3x + 3 ha slope 3 and y-intercept 3.

Start at 3 on the y-axis and mark a point. Then from this point move up 3 units and to the right 1 unit. Mark a point and connect.

y=-x - 3 has slope -1 and y-intercept -3.

Start at -3 on the y-axis and mark a point. Then from this point move down 1 unit and to the right 1 unit. Mark a point and connect.

This graph is represented in the picture attached.

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Which graph represents the following system of equations?

y = 3x + 3

y = –x – 3

...............................................................................................................................................

y=x−8

​y=12x−5​

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Graph of 2 lines that intersect at one point. Both lines are solid. One line passes through (-2,2) and (0,3) and is shaded below the line.

y < = 1/2x + 3...(-2,2) y < = 1/2x + 3....(0,3)

2 < = 1/2(-2) + 3 3 < = 1/2(0) + 3

2 < = -1 + 3 3 < = 0 + 3

2 < = 2 (correct) 3 < = 3 (correct)

The other line passes through points (0,1) and (1,-2) and is shaded above the line.

y > = -3x + 1...(0,1) y > = -3x + 1...(1,-2)

1 > = -3(0) + 1 -2 > = -3(1) + 1

1 > = 0 + 1 -2 > = -3 + 1

1 > = 1 (correct) -2 > = -2 (correct)

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we have

using a graph tool

see the attached figure

The solution of the system is the shaded area

we know that

The line is solid

The line passes through points and and is shaded above the line.

The line is solid

The line passes through points and and is shaded below the line

The two lines intersect at one point

therefore

the answer is the option

B) Graph of two lines that intersect at one point. Both lines are solid. One line passes through points negative 2, 2 and 0, 3 and is shaded below the line. The other line passes through points 0, 1 and 1, negative 2 and is shaded above the line.

Answer 2

Answer: Graph D (bottom right corner)

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Step-by-step explanation:

The equation y = 3x+3 is in slope intercept form y = mx+b

m = 3 = slope

b = 3 = y intercept

In this case, both the slope and y intercept are the same (though in general they tend not to be).

The positive slope value means the line goes uphill as you move from left to right. The positive y intercept means the diagonal line crosses the y axis somewhere above the horizontal x axis. Specifically, it crosses the y axis at y = 3

Graph D is the only graph that has such a line on it. Graphs A, B and C have the positive slope line where they have a negative y intercept, so we can rule them out.

You can use graphing tools such as Desmos or Geogebra to help confirm this answer. You could also make a table of values, and plot each point, to form the lines. Two points is the minimum amount needed to form any line.