Linear Functions

Identifying Linear Functions

100

What is a function whose graph forms a straight line called?

linear function

200

What is the general form of a linear equation?

ax + by + d= 0

300

Tell whether the function is linear and turn it into general form of linear equation: y=3/2x+6

Yes can be written as 6x - 4y + 24 = 0

400

Tell whether the set of ordered pairs is a linear function, and write the equation in gradient-intercept form. (0,4), (2,7) (4,10), (6,13)

Yes, linear. y=6/4x+4

500

Tell whether the function is linear and graph the function: f(x) = -6x + 2

Yes it is linear.

Gradients and Intercepts

100

What is the x-coordinate of the point where the graph intersects the x axis called?

What is the x intercept

200

What is the relationship between the gradients of perpendicular lines?

opposite reciprocal gradients 

OR

m₁ x m₂ = -1

300

What lines have the same gradient?

parallel

400

Find the x and y intercepts of 2x + 4y=8.

x=4 and y=2

500

Find the x and y intercepts of 3x- 2y=12

x=4 and y=-6

Gradient

100

What is the gradient of a horizontal line?

Zero

200

What is the gradient of a vertical line?

Undefined

300

Find the gradient of (4,-2) and (-1,2)

What is -4/5

400

Find the gradient of the equation: 6x + 5y=30

-6/5

500

Find the gradient of (20,3000) and (60,2000)

What is -25

Gradient-Intercept Form

100

What is gradient-intercept form?

y=mx+b

200

Write the equation in gradient-intercept form of a line whose gradient is 0 and y-intercept is (0, -5).

y=-5

300

Write the equation in gradient-intercept form of a line whose gradient is 2/3 and passes through the point (3,-2). 

y=2/3x-4

400

Graph the equation: y= 4x-3

500

Write the equation in gradient-intercept form: 3x+2y=8

y=-3/2x+4 

Point-Gradient Form

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

The product of the gradient of two perpendicular lines is 

What is -1 

300

Write an equation of a line in point-gradient form that passes through the points (-5, 3) and (4, -6).

y - 3 = 1(x +5)

OR

y + 6 = 1(x -4)

400

Write this equation in point-gradient form AND in gradient-intercept form: gradient = -5, (-1,-2)

y + 2= -5(x+1)   AND   y = -5x -6

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)