Question

Identify the system of equations given in the graph below.

Answer 1

Hi there!

$\large\boxed{\left \{ {{y=3x + 1} \atop {y = 3x - 1}} \right}$

From the graph, we can see that both lines are parallel. We can determine the slope of one line to find the slope of the other.

Use the slope formula to determine the slope of a line. In this case, I am using the blue line as a reference:

$\text{Slope } = \frac{ y_2 - y_1 } { x_2 - x_1 }$

$m = \frac{ 3 - 1 } { 1 - 0 } = 3$

The slope of both lines is 3.

Let's find the equation of the blue line by finding its y-intercept to solve for the "b" value in the equation y= mx + b:

y-intercept is when x = 0, or at (0, 1). Therefore:

Blue line equation: y = 3x + 1

The red line intersects the y-axis at (0, -1), therefore:

Red line equation: y = 3x - 1

The systems of equations is:

y = 3x + 1

y = 3x - 1