Question

quiz slope intercept form and gra determine if each statement is true or false the system has infinitely many solutions the y - intercept of the light blue line is (0, 7) the lines are descending the slope of the dark blue line is 3/2 the lines are parallel this system has no solution the lines have different slopes the equation of the light blue line is y = -3/2x + 7 the equation of the dark blue line is y = -3/2x

Explanation:

Step1: Analyze number of solutions

Two non - parallel lines intersect at a single point. Since the lines in the graph are non - parallel, they are not the same line, so the system does not have infinitely many solutions. False.

Step2: Find y - intercept of light blue line

The light blue line crosses the y - axis at the point (0, 7). So the y - intercept of the light blue line is (0, 7). True.

Step3: Check line direction

As we move from left to right, the lines go downwards, so the lines are descending. True.

Step4: Calculate slope of dark blue line

The dark blue line has a negative slope. If we take two points on the dark blue line, say (0, 1) and (2, - 2), the slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-2 - 1}{2-0}=-\frac{3}{2}
eq\frac{3}{2}$. False.

Step5: Check for parallel lines

The lines intersect, so they are not parallel. False.

Step6: Analyze number of solutions again

Since the lines intersect at a single point, the system has a single solution, not no solution. False.

Step7: Check slopes

The slopes of the two lines are different. The light blue line has a slope of $-\frac{3}{2}$ and the dark blue line has a different negative slope. True.

Step8: Find equation of light blue line

The slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. The light blue line has a slope of $-\frac{3}{2}$ and y - intercept of 7, so its equation is $y=-\frac{3}{2}x + 7$. True.

Step9: Assume equation of dark blue line

Let's assume the dark blue line has a slope $m_1=-\frac{3}{2}$ (wrong assumption as we calculated it above) and y - intercept $b_1 = 1$, its equation is not the same as the light blue line's equation.

Answer:

The system has infinitely many solutions: False
The y - intercept of the light blue line is (0, 7): True
The lines are descending: True
The slope of the dark blue line is 3/2: False
The lines are parallel: False
This system has no solution: False
The lines have different slopes: True
The equation of the light blue line is y=-3/2x + 7: True
The equation of the dark blue line (not fully given in question but based on analysis): Different from light blue line's equation