Systems of Equations
One line has a slope of 0, the other's slope is undefined. What are the possible solutions?
1. They are vertical lines (undefined slope) and horizontal lines (slope of 0).
The diameter of a circle joins the points C(-7, -4) and D(-1, 10). What are the coordinates of the centre of the circle?
(-4, 3)
What is the domain and range of this graph? Is it a function?
D = {x|x≥0, x∈R}
R = {y∈R}
Write an equation in standard form for the line through the given points: (5, 3) and (2, 3). What will the graph look like?
x = 2. The line is vertical, passes through point 2 on the x-axis and the slope is undefined.
Determine whether the point P(4,−2) lies on the perpendicular bisector of the line segment with endpoints A(3,5) and B(−3,−1).
It does lie on the line.
If (2,3) and (-3,5) are both solutions to a system of two linear equations, does the system have any other solutions? Explain.
If there are two solutions, then there must be an infinite number of solutions
Determine an equation of a circle with a diameter of 16 and centered at (0,0).
x2+y2=64
State whether this set of ordered pairs represents a function: {(-2, 5), (-3, 7), (-2, 9), (-4, 11)}
Not a function.
Write an equation in standard form for the line through the given points: L(0, 4) and M(-3, 0).
4x-3y+12=0
Determine an equation in standard form for the right bisector of the line segment joining A(3, 6) and B(-1, 2).
x+y-5=0
Without graphing the equations, state whether the system of equations has one solution, no solution, or infinite solutions.
x - y = 6
2x - 2y = -4
Parallel and distinct, therefore no solutions
Write the coordinates of the midpoint between the following points: (4a, 3b) and (8a, -b)
(6a, b)
What is the domain and range of this graph? Is it a function?
D = {x|-3≤x<4, x∈R}
R = {y|-5≤y<6, y∈R}
Is a function.
Determine an equation for the following line (in standard form): the line perpendicular to x+2y-8=0 and passing through the point (-3, -4).
2x-y+2=0
Determine an equation in standard form for the right bisector of the line segment joining A(3, 6) and B(-1, 2).
x+y-5=0
Write an equation that forms a system of equations in which there are infinitely many solutions with x+y=5.
y = -x + 5
A coast guard patrol boat is located 5 km east and 8 km north of the entrance to St. John’s harbour. A tanker is 9 km east and 6 km south of the entrance. Find the distance between the two ships, to the nearest tenth of a kilometre.
14.6 km
Observe the graph on the board. What is the domain and range? Is this a function?
D = {x|-5≤x≤5, x∈R}
R = {y|-5≤y≤5, y∈R}
Not a function.
Write an equation in standard form for the line through the given points: G(-2, -3) and H(3, -1)
2x-5y-11=0
ABC has vertices A(3, 4), B(-5, 2), and C(1, -4). Determine an equation in standard form for:
CD, the median from C to AB.
7x+2y+1=0
Identify the ordered pair that satisfies both equations:
y=2x+15
y=-2x-1
(-4,7)
A park is in the shape of a circle that is represented by the equation x2+y2=64. The park was designed to have a circular rose garden at the centre, concentric with the park and represented by the equation x2+y2=16. Determine the area of the park that does not contain roses.
A = 48 pi
Observe the graph drawn on the board. The equation of the function is y = 1/x. What is the domain and range?
D = {x|x≠0, x∈R}
R = {y|y≠0, y∈R}
Write an equation in standard form for the line through the given points: L(0, 4) and M(-3, 0)
4x-3y+12=0
Find the area of a triangle with vertices E(1,3)E(1,3), F(−4,−3)F(−4,−3), and G(5,−4)
29.5 units