Identifying Linear Functions
Gradients and Intercepts
Gradient
Gradient-Intercept Form
Point-Gradient Form
100
What is a function whose graph forms a straight line called?
linear function
100
What is the x-coordinate of the point where the graph intersects the x axis called?
What is the x intercept
100
What is the gradient of a horizontal line?
Zero
100
What is gradient-intercept form?
y=mx+b
100
Write the linear equation in point-gradient form with a gradient of -7 and passes through the point (4,2)
y-2 = -7(x -4)
200
What is the general form of a linear equation?
ax + by + c = 0
200
What is the relationship between the gradients of perpendicular lines?
opposite reciprocal gradients
OR
m1 x m2 = -1
200
What is the gradient of a vertical line?
Undefined
200
Write the equation in gradient-intercept form of a line whose gradient is 0 and y-intercept is (0, -5).
y=-5
200
What lines have the same slope?
parallel
300
Tell whether the function is linear and turn it into general form of linear equation: y=(3/5)x+3
Yes can be written as 3x - 5y + 15 = 0
300
What lines have the same gradient?
parallel
300
Find the gradient of (4,-2) and (-1,2)
What is -4/5
300
Write the equation in gradient-intercept form of a line whose gradient is 4 and passes through the point (2,5).
y=4x-3
300
Write an equation of a line in point-gradient form that passes through the points (4, 3) and (-5, -6).
y - 3 = 1(x - 4)
OR
y + 6 = 1(x + 5)
400
Tell whether the set of ordered pairs satisfies a linear function. Explain. (2,4), (5,3) (8,2), (11,1)
Yes, constant change in 3 for x. Constant change of -1 in y
400
Find the x and y intercepts of 3x- 2y=12
x=4 and y=-6
400
Find the gradient of (20,3000) and (60,2000)
What is -25
400
Graph the equation: y= 4x-3
400
Write this equation in point-gradient form AND in gradient-intercept form: gradient = -4, (-1,-2)
y + 2= -4(x+1) AND y = -4x -6
500
Tell whether the function is linear and graph the function: f(x) = -6x + 2
Yes it is linear.
500
Find the x and y intercepts of 2x + 4y=8.
x=4 and y=-2
500
Find the gradient of the equation: 6x + 5y=30
-6/5
500
Write the equation in gradient-intercept form: 3x+2y=8
y=(-3/2)x+4
500
Write the equation in point-gradient form TWO WAYS that passes through these points: (1,-4) and (3,2)
y - 2 = 3(x - 3)
AND
y + 4 = 3(x - 1)