I’ll give brainliest

The graph of the system of equations solves the equation   x - 4 = -2x + 1 ⇒ D

Step-by-step explanation:

Let us revise some important notes about the slope and y-intercept of a line

The form of the linear equation is y = m x + b, where m is the slope and b is the y-intercept

The y-intercept (0, b) is the the point of intersection between the line and the y-axis

To solve our question without any calculation, let us find the direction of the slopes and their y-intercepts

∵ The direction of the blue line is to the left

→ That means m in the equation is negative

∴ Its slope is negative

∵ The line intersects the y-axis at point (0, 1)

→ That means b in the equation = 1

∴ The number in the equation is 2

→ Look at the answer we have only one answers have negative slope and

   y-intercept = 1 in the right hand side ⇒ D

∴ The equation of the blue line is represented by the left side -2x + 1

→ That means the equation of the red line is represented by the left side

∵ The direction of the red line is to the right

→ That means m in the equation is positive

∴ Its slope is positive

∵ The line intersects the y-axis at point (0, -4)

→ That means b in the equation = -4

∴ The number in the equation is -4

→ Only D has a positive slope and y-intercept = -4 in the left side

∴ The equation of the red line is represented by x - 4

The graph of the system of equations solves the equation   x - 4 = -2x + 1

Another way:

You can solve each equation to find the value of x, then substitute it in one side of the equation to find y , the values of x and y must be (2, -3) as the point of intersection of the two lines in the graph

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step-by-step explanati∵∵∴∴on:

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24