Gradient
What is the gradient in y = mx + c ?
Gradient = m
What does 'x intercept' mean ?
The x-intercept is the point where a line crosses the x-axis.
When y = 0
Label all parts of:
y = mx + c
y = y coordinate
m = gradient
x = x coordinate
c = y intercept
Transpose y = 5x - 3 to make (x) the subject
x = (y+3) / 5
Bertha knits teddy bears and sells them at the local farmers’ market. Bertha spends $120 in wool, and it costs her an additional $4.50 to make each teddy bear. She sells the bears for $14.50 each. How many teddy bears does Bertha need to sell to cover her costs?
Number of teddy bears = 12
What is the formula to calculate the gradient? (hint: not just 'rise/run')
m = (y2-y1) / (x2-x1)
What does 'y intercept' mean?
The y-intercept is the point where a line crosses the y-axis.
x = 0
What is the line that passes through the point (2,−1) ?
x + y = 1
Transpose and make y the subject of:
8x = -3y - 12
y = (8x+12)/-3 or y = -8/3x - 4
A person leaves home and travels to work. If it takes them 45 minutes to travel 50km, how fast were they travelling? (assuming they travel the same speed constantly)
Additionally, which part does this represent in the equation y = mx + c ?
Speed = 50km/ 45min
= 50km/0.75hours
= 66.67km/hour and represents the gradient
What is the gradient of the line passing through the points (4,6) and (−2,−6)?
Gradient = 2
What are the x and y intercepts of the linear graph with equation 3x−y=6 ?
(2, 0) and (0, -6)
What is the equation of a straight line passing through the points (−2,3) and (5,1)?
y = -2/7x + 17/7
An inflated party balloon has a small hole and is slowly deflating. The initial volume of the balloon is 1000 cm3 and the balloon loses 5 cm3 of air every minute.
If V represents the volume of the balloon in cm3 and t represents the time in minutes, what is the equation to represent the volume of the balloon after t minutes ?
v = 1000 - 5t
A 1000L tank currently has 240L of water. How long will it take to fill the tank using a pump that pumps out 25L/min ?
Time to fill the tank = 30.4 minutes or 30minutes and 24 seconds
Find the gradient of the line passing through the following pairs of points:
(3, -2) and (0, 4)
Gradient = -2
What is the y intercept of:
y = 3x - 1
(0, -1)
What is the gradient of the equation:
-2x + 4y = 6
Gradient = 1/2
Transpose and make y the subject of:
3x - 4y + 7 = 10
y = 3/4x - 3/4 or y = (3x-3)/4
Tommy is saving for a remote-controlled car that is priced at $49. He has $20 in his piggy bank. Tommy saves $3 of his pocket money every week and puts it in his piggy bank. The amount of money in dollars, M, in his piggy bank after w weeks can be found using the rule M=3w+20.
How many weeks will it take for Tommy to have saved enough money to purchase the remote-controlled car?
10 weeks
A line has a gradient of −3/4. If the line passes through the points (−a,3) and (−2,6), find the value of 'a'.
a = -2
What is the x intercept of:
y = 3x - 1
(1/3, 0)
What is the equation of the line that passes through the points (7, 2) and (2, 12)?
y = -2x+16
Determine the value of x:
(3x + 4)/2 + (x+1)/3 = 6
x = 2
Miriam has a sweet tooth, and her favourite sweets are strawberry twists and chocolate ripples. The local sweet shop sells both as part of their pick and mix selection, so Miriam fills a bag with them. Each strawberry twist weighs 5 g and each chocolate ripple weighs 9 g. In Miriam’s bag there are 28 sweets, weighing a total of 188 g. Determine the number of each type of sweet that Miriam bought by forming and solving a linear equation.
16 strawberry twists and 12 chocolate ripples