Susie determined that the system of equations below has infinitely many solutions.
The first line goes through the points (2, -13) and (-2, -1).
The second line goes through the points (5, -22) and (-3, 2).
Is she correct? Use your Desmos calculator
(1 point)
• Yes, Susie is correct.
• No, there is no point of intersection.
• She may or may not be correct as the lines possibly cross.
• No, the lines are parallel
To determine if Susie is correct, we can graph the system of equations using a Desmos calculator.
The first line can be represented by the equation: y = -3x - 7
The second line can be represented by the equation: y = -4x - 2
Graphing these two equations, we can see that the lines do intersect at the point (-2, -1). Therefore, Susie is correct in saying that the system of equations has infinitely many solutions.
The answer is: Yes, Susie is correct.
To determine if Susie is correct, we can use the Desmos calculator to graph the system of equations and see if the lines intersect or are parallel.
The equation of the first line can be written in point-slope form as y - y₁ = m(x - x₁). Using the given points (2, -13) and (-2, -1), we can find the slope as m = (y₂ - y₁)/(x₂ - x₁) = (-1 - (-13))/(-2 - 2) = 12/-4 = -3. Thus, the equation of the first line is y - (-13) = -3(x - 2).
Similarly, the equation of the second line can be written as y - y₁ = m(x - x₁) using the points (5, -22) and (-3, 2). The slope is m = (2 - (-22))/(-3 - 5) = 24/-8 = -3. Therefore, the equation of the second line is y - (-22) = -3(x - 5).
Using the Desmos calculator, let's plot these equations.
The graph shows that the two lines are indeed overlapping, meaning they have infinitely many points of intersection. Therefore, Susie is correct in stating that the system of equations has infinitely many solutions. The answer is: Yes, Susie is correct.
To determine whether Susie is correct and the system of equations has infinitely many solutions, we can use a Desmos calculator. Here's how you can do it:
1. Go to the Desmos website or open the Desmos app
2. Click on the "+" symbol to create a new graph or open a new graph if you already have one.
3. Enter the first equation in the form of "y = mx + b". For the first line, since it goes through the points (2, -13) and (-2, -1), you can use the point-slope formula to find the equation. Given 2 points (x1, y1) and (x2, y2), the formula is:
y - y1 = m(x - x1)
Plug in the values: x1 = 2, y1 = -13, x2 = -2, y2 = -1
y - (-13) = m(x - 2)
Simplify: y + 13 = m(x - 2)
4. Enter the second equation using the same method. Given the points (5, -22) and (-3, 2), the equation becomes:
y - (-22) = m(x - 5)
Simplify: y + 22 = m(x - 5)
5. After entering both equations, the Desmos graph should show the lines plotted. Look for any point of intersection between the lines.
6. If there is a point of intersection, Susie is incorrect and the system of equations does not have infinitely many solutions.
7. If the lines are parallel and do not intersect, Susie is also incorrect.
8. However, if the lines are the same and perfectly overlap, Susie is correct, and the system of equations has infinitely many solutions.
By following these steps and using the Desmos calculator, you should be able to determine whether Susie is correct or not.