To determine whether the system of equations has infinitely many solutions, we can graph the equations and see if the lines intersect at more than one point.
For the first line, we can use the two given points to find its equation.
The slope of the line is {(y2-y1)/(x2-x1) = (-1-(-13))/(-2-2) = 12/4 = 3}.
Using the point-slope form of a line, we can write the equation as:
y - y1 = m(x - x1),
where m is the slope and (x1, y1) is any point on the line.
Using the point (2, -13), the equation can be written as:
y + 13 = 3(x - 2),
which simplifies to:
y = 3x - 6 - 13,
y = 3x - 19.
For the second line, we can again use the two given points to find its equation.
The slope of the line is {(y2-y1)/(x2-x1) = (2-(-22))/(-3-5) = 24/(-8) = -3}.
Using the point-slope form of a line, we can write the equation as:
y - y1 = m(x - x1).
Using the point (5, -22), the equation can be written as:
y + 22 = -3(x - 5),
which simplifies to:
y = -3x + 15 - 22,
y = -3x - 7.
Now we can graph the two equations on the Desmos calculator to see if they intersect at more than one point.
Based on the graph, we can see that the two lines intersect at exactly one point (-1, -4), indicating that the system of equations does not have infinitely many solutions.
Therefore, Susie is incorrect.
Susie determined that the system of equations below has infinitely many solutions. %0D%0A%0D%0AThe first line goes through the points (2, -13) and (-2, -1).%0D%0A%0D%0AThe second line goes through the points (5, -22) and (-3, 2).%0D%0A%0D%0AIs she correct? *Use your Desmos calculator%0D%0A%0D%0A(1 point)
1 answer