Susie determined that the system of equations below has infinitely many solutions. The first line goes through the points, two and -13 and -2 and negative one the second one goes through the points five and -22 and -3 and two is she correct? A no the lines are parallel be she may or may not be great as a lot of possibly cross say no there is no point of intersection or d . Yes, Susie is correct.
No, the lines are not parallel and do have a point of intersection. Susie is correct.
To determine if Susie is correct or not, we need to find the slopes of both lines and compare them.
The first line goes through the points (2, -13) and (-2, -1). We can use the formula to find the slope:
slope = (y2 - y1) / (x2 - x1) = (-1 - (-13)) / (-2 - 2) = 12 / (-4) = -3
The second line goes through the points (5, -22) and (-3, 2). Again, we can find the slope:
slope = (y2 - y1) / (x2 - x1) = (2 - (-22)) / (-3 - 5) = 24 / (-8) = -3
The slopes of both lines are the same, -3.
Since the slopes are equal, the lines are parallel, and they will not intersect at any point. This means that Susie is incorrect in stating that the system of equations has infinitely many solutions. The correct answer is: A) No, the lines are parallel; there is no point of intersection.
To determine if Susie is correct, we need to check if the two lines are parallel or if they intersect at a point. Let's break it down step by step.
First, let's write the equations of the two lines using the given points.
The equation for the first line passing through the points (2, -13) and (-2, -1) can be derived as follows:
Step 1: Find the slope (m) of the line using the formula m = (y2 - y1)/(x2 - x1).
m = (-1 - (-13))/(-2 - 2) = 12/-4 = -3
Step 2: Now that we have the slope, we can use the point-slope form of a line. Let's use the first point (2, -13).
y - y1 = m(x - x1)
y - (-13) = -3(x - 2)
y + 13 = -3x + 6
y = -3x - 7
So, the equation of the first line is y = -3x - 7.
Now, let's do the same for the second line passing through the points (5, -22) and (-3, 2):
Step 1: Find the slope (m) of the line using the formula m = (y2 - y1)/(x2 - x1).
m = (2 - (-22))/(-3 - 5) = 24/-8 = -3
Step 2: Using the point-slope form of a line with the first point (5, -22):
y - y1 = m(x - x1)
y - (-22) = -3(x - 5)
y + 22 = -3x + 15
y = -3x - 7
So, the equation of the second line is y = -3x - 7.
Now, let's compare the two equations:
y = -3x - 7 (equation of the first line)
y = -3x - 7 (equation of the second line)
Both equations have the same slope (-3) and y-intercept (-7). It means that the lines are identical. Therefore, they are not only intersecting at a single point but for every possible (x, y) combination. Hence, they have infinitely many solutions.
So, Susie is correct in stating that the system of equations has infinitely many solutions.