Answer:
The graph of the system of equations solves the equation [tex]\frac{1}{2}[/tex] 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
- If the line has a positive slope then its direction will be to the right
- If the line has a negative slope then its direction will be to the left
The y-intercept (0, b) is the the point of intersection between the line and the y-axis
- If the line cuts the y-axis at a point above the x-axis, then b is positive
- If the line cuts the y-axis at a point down the x-axis, then b is negative
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 [tex]\frac{1}{2}[/tex] x - 4
The graph of the system of equations solves the equation [tex]\frac{1}{2}[/tex] 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
