Oliver and marie are graphing two equations on a coordinate grid. oliver has graphed the equation y = 2x + 2. if marie graphs y = 2x - 3, where will the y-intercept of her graph be in relation to oliver's graph? a) 3 units lower b) 5 units lower c) 5 units higher d) the same place

B) 5 units lower.

Step-by-step explanation:

We have been given that Oliver has graphed the equation and Marie graphs . We are asked to find where Marie's graph will be with relation to Oliver's graph.

We can see that both lines are in slope-intercept form of equation: , where,

m = Slope of the line,

b = Initial value or y-intercept.

We can see that both lines have same slope, but y-intercepts for both lines are different.

Since y-intercept is the point, where line crosses y-axis. We can see that Oliver's line will cross y-axis at y=2, while Marie's line crosses y-axis at y=-3.

Since -3 is 5 units below from 2, therefore, y-intercept of Marie's graph be 5 units lower than Oliver's graph and option B is the correct choice.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.