Question

1. determine whether the system of linear equations below has one solution, infinitely many solutions, or no solution.

-6x - 9y = 0
-24x = 36y

1. this scatter plot shows the relationship between the number of weeks a student has been saving money and the total balance in the student’s savings account.

savings account balance vs. weeks of saving
the y-intercept of the estimated line of best fit is at (0, b). enter the approximate value of the b in the first response box:
enter the approximate slope of the estimated line of best fit in the second response box:

Explanation:

Question 6

Step1: Rewrite equations in slope-intercept form

For the first equation \(-6x - 9y = 0\), solve for \(y\):
\(-9y = 6x\)
\(y = -\frac{6}{9}x = -\frac{2}{3}x\)

For the second equation \(-24x = 36y\), solve for \(y\):
\(y = \frac{-24}{36}x = -\frac{2}{3}x\)

Step2: Analyze the equations

Both equations simplify to \(y = -\frac{2}{3}x\), meaning they are the same line.

Step1: Find the y-intercept (\(b\))

The y-intercept is the value of \(y\) when \(x = 0\). From the graph, the line of best fit crosses the \(y\)-axis at \((0, 50)\), so \(b = 50\).

Step2: Calculate the slope

Slope \(m = \frac{\text{change in } y}{\text{change in } x}\). Use two points on the line, e.g., \((0, 50)\) and \((12, 350)\):
\(m = \frac{350 - 50}{12 - 0} = \frac{300}{12} = 25\) (or use other points, e.g., \((4, 150)\): \(m = \frac{150 - 50}{4 - 0} = \frac{100}{4} = 25\)).

Answer:

infinitely many solutions

Question 7