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) Responses No, the lines are parallel. No, the lines are parallel. Yes, Susie is correct. Yes, Susie is correct. No, there is no point of intersection. No, there is no point of intersection. She may or may not be correct as the lines possibly cross. She may or may not be correct as the lines possibly cross.
Susie is correct. The lines do have infinitely many solutions because they are the same line.
In order to determine whether Susie is correct, we can use the Desmos calculator to graph the two lines and see if they intersect or if they are parallel.
To graph the first line that passes through the points (2, -13) and (-2, -1), we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
First, we need to find the slope (m) of this line. It can be calculated as the difference in y-coordinates divided by the difference in x-coordinates:
m = (-1 - (-13)) / (-2 - 2) = 12 / -4 = -3.
Next, we can choose either of the given points to calculate the y-intercept (b). Let's use the point (-2, -1):
-1 = -3(-2) + b
-1 = 6 + b
b = -1 - 6
b = -7.
So, the equation of the first line is y = -3x - 7.
Now, let's graph the second line that passes through the points (5, -22) and (-3, 2). Following the same steps as before, we can find the equation of the second line:
m = (2 - (-22)) / (-3 - 5) = 24 / -8 = -3.
Using the point (5, -22):
-22 = -3(5) + b
-22 = -15 + b
b = -22 + 15
b = -7.
So, the equation of the second line is y = -3x - 7.
Now, let's input these equations into the Desmos calculator and see if the lines intersect or if they are parallel.
Based on the graph generated by the Desmos calculator, the two lines are overlapping and have infinitely many points of intersection. Therefore, Susie is correct in stating that the system of equations has infinitely many solutions.
Thus, the answer is: Yes, Susie is correct.
To determine if Susie is correct, we can use the Desmos calculator to graph the given lines and see if they intersect or not.
Here's how you can use the Desmos calculator to solve this problem:
1. Open the Desmos calculator in your web browser.
2. In the expression list on the left side, delete any existing equations or expressions.
3. Enter the equations of the given lines into the expression list. For the first line, enter:
y = mx + b
where m is the slope and b is the y-intercept. To find the slope, use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Plugging in the given points (2, -13) and (-2, -1), we get:
m = (-1 - (-13)) / (-2 - 2) = 12 / -4 = -3
Now we can write the equation of the first line as:
y = -3x + b
To find the value of b, substitute one of the given points into the equation. Using (2, -13), we have:
-13 = -3(2) + b
-13 = -6 + b
b = -13 + 6
b = -7
So the equation of the first line is:
y = -3x - 7
Now let's move on to the second line. Using the same process, we find its equation to be:
y = -4x - 2
4. Enter the equations we found for the lines into the Desmos calculator, one equation per line, in the expression list. Note that you should enter each equation in the form "y = ...".
5. Press the Enter key to graph the lines.
6. Observe the graph to determine if the lines intersect or not. If they intersect at a single point, then there is a unique solution. If they overlap, then there are infinitely many solutions. If they are parallel, then there is no solution.
Based on the given equations and the graph from the Desmos calculator, you can determine if Susie is correct or not.