Slope/Gradient
The formula for calculating the gradient/slope:
rise/run or (y2-y1)/(x2-x1)
What is the y intercept of the line y=2x+4
(0, 4)
The standard form of a linear equation is
y = mx + c
Graph x=-2 and y=3
x=-2 vertically
y=3 horizontally
What is the mid point of (2,4) and (6,2)
Midpoint = (4,3)
What is the gradient/slope of the line y=x+4
m = 1
Find the y-intercept of 3x + 4y = 24.
(0,6)
The gradient and y-intercept of y = -2x - 3
m = -2, c = -3
Sketch y = -3x + 5 (show x,y-intercept)
c= -2 (turning point)
Min as coefficient of x is positive
x intercepts (-1,0) and (1.0)
What is the distance between (5,5) and (1,7)
The distance between those 2 points is 4.47 units
Find the gradient/slope of the line 2y-2x=7
m = 1
What is the y intercept of the line 4y-2x=16
(0,4)
An equation with a gradient of -4 and y-intercept of 5 is written...
y = -4x + 5
Graph y=-2x-3 using the x and y intercept method.
x-intercept of (-1.5,0)
y-intercept of (0, -3)
Negative gradient
What is the gradient of a line that passes through (-2,1) and (-1,3)
m=2
Find the gradient/slope of the line 3x+2y=0
m = -3/2 or -1.5
Find the y intercept of -2x +8y = -8
(0,-1)
What is the equation of a line with a gradient of 0 that passes through the point (1, 2)
y=2
sketch y=2x+3
y intercept at 3
gradient is 2 up 1 across
What is the midpoint of (3, -9) and (8, 4)
M(5.5, -2.5)
Find the gradient od a line with the y intercept of 4 and that passes through (2,2)
m= -1
what is the y intercept of the line x=2
there is no y intercept
A personal assistant charges $50 for an initial consultation plus $15 per hour. Write a rule for this and find the charge for a 4 hour consultation.
y = 15x +50 let x = 4
y = 15 x 4 +50
y=110.
Therefore, the personal assistant charges $110 for a 4 hour consultation.
Sketch
y=2/3 x+2
y intercept = 2
gradient 2 up 3 across
What is the distance and midpoint of the following:
(-2, 6) and (6, -4)
D = 12.81
M(2, 1)