Slope
What is the slope of y = (3/2)x + 5?
(3/2)
A line that passes through the origin has a slope of 3. Write one more point that is on the line.
Some possibilities: (1, 3), (2, 6), (3, 9), (-1, -3), (-2, -6), (-3, -9), ...
The value of y varies directly with x, and the constant of variation equals 4. Find the value of y when x = 25.5.
y = 102
If x and y vary inversely, find the constant of variation when y = -12 and x = -6.
Find the x- and y-intercept for the following linear function:
5x - 3y = 3
(3/5, 0) and (0, -1)
What is the slope of y = -5x - 2?
-5
A line that passes through the point (2, 0) has a slope of (3/4). Write two more points on the line.
Some possibilities: (6, 3), (10, 6), (14, 9), (-2, -3), (-6, -3), (-10, -6), ...
The value of y varies directly with x. Find the constant of variation when y = 45 and x = 9.
k = 5
If x and y vary inversely, write an inverse variation equation when x = 7 and y = 0.5.
y = (3.5)/x
Determine the value of t so that the line has the given slope.
(t, 5), (5, 1); slope = -2
3
Write a direct variation equation that has a slope of 3.
y = 3x
A line passes through the point (3, 2) and has slope of (-2). Write two more points on the line.
Some possibilities: (4, 0), (5, -2), (6, -4), (2, 4), (1, 6), (0, 8), ...
The value of y varies directly with x, and when y = 36, x = 3. Write a direct variation equation.
y = 12x
The value of y varies indirectly with the value of x. Write an indirect variation equation for when y = 3 and x = 16. Then solve for y when x = 5.
y = 48/x
y = (48/5) = 9.6
Determine if the following points are collinear. IF they are collinear, find the slope.
(0,3), (1,5), (2,7), (3,9)
collinear; 2
A graph shows a line starting at the origin and passing through the point (5, 4). What is the slope of this line?
The school cafeteria ordered 45 pounds of beef for $360, not including the delivery charge. If the beef company charges a flat fee of $72 for delivering the beef, what is the total cost (including the delivery charge) of ordering 55 pounds of beef?
$512
The value of y varies directly with x, and when y = -30, x = 10. Write a direct variation equation, then find the value of y when x = 5.
y = -3x
y = -15 (when x = 5)
If volume and pressure vary inversely, and the volume is 32 cm3 when the pressure is 4 pounds, what is the pressure when the volume is 8 cm3?
P = 16 pounds
Determine if the following points are collinear. IF they are collinear, find the slope.
(-3, 5), (-3, 3), (-3, 1), (-3, -1)
Collinear; no slope
A line passes through points (-1, -2) and (0, 4). What is the slope of this line?
6/1 = 6
If a graph shows two points with coordinates (-2, 5) and (4, -11), what is the slope of a line drawn through both points?
Slope = -(8/3)
The value of y varies directly with x, and when y = 0.5, x = 2. Write a direct variation equation, then find the value of y when x = 5.
y = 0.25x
y = 1.25 (when x = 5)
The volume of air inside a balloon varies indirectly with the pressure of air. If the volume is 23 cm3 when the pressure is 9 pounds, find the volume when the pressure is 13 pounds. Round to the nearest whole number.
V = 16 cm3
Write the following linear equation in standard form.
1.25x + 7.5 = y
5x - 4y = -30