Linear Functions and Graphs

​4 /

Finding Expressions for Linear Functions

(Writing Equations: y=mx+b)

​4 /

Finding Expressions for Linear Functions

*slope

*y-intercept

*a point along the graph

y=mx + b

Practice

Multiple Choice

Identify the gradient and y-intercept of the linear graph:

y = 2x + 1

• gradient: 1

  y-intercept: 2

• gradient: 2

  y-intercept: 1

• gradient: -1

  y-intercept: -2

• gradient: -2

  y-intercept: -1

Fill in the Blanks

Multiple Choice

Identify the gradient and y-intercept of the linear graph:

y = -2x - 1

• gradient: 1

  y-intercept: 2

• gradient: 2

  y-intercept: 1

• gradient: -1

  y-intercept: -2

• gradient: -2

  y-intercept: -1

Fill in the Blanks

Multiple Choice

Identify the gradient and y-intercept of the linear graph:

y = - 4 + x

• gradient: 4

  y-intercept: 1

• gradient: -4

  y-intercept: 1

• gradient: 1

  y-intercept: 4

• gradient: 1

  y-intercept: -4

Fill in the Blanks

Multiple Choice

When a linear graph has a up slope, what will the gradient be?

• positive gradient

• negative gradient

Fill in the Blanks

Multiple Choice

When a linear graph has a down slope, what will the gradient be?

• positive gradient

• negative gradient

Practice Problems

p.66

Open Ended

Find the expression for the linear function:

(1) The graph is a line that passes through point (2 , -1) and has a slope of 3

Open Ended

Find the expression for the linear function:

(2) The rate of change is -5 and y=3 when x=2

Open Ended

Find the expression for the linear function:

(3) y=2 when x=-3, and the increase in y is 5 when x increases by 3

Open Ended

Find the expression for the linear function:

(4) The graph is a line that passes through the point (0,5) and is parallel to the graph of $$y=\frac{2}{3}x$$

Open Ended

Find the expression for the linear function:

(5) The graph is a line that passes through the points (0, -2) and (4,1)

Open Ended

Find the expression for the linear function:

(6) y=2 when x = -2, and y=8 when x=2

​*** slope and intercept

• The line passes through the point (0, 3)

• This would mean that the intercept is +3

• y = mx + b; b is + 3

​*** slope and intercept

​*** slope and intercept

​intercept (b): + 3

slope (m): 1

• y = mx + b; m = 1 and b = +3

• y = 1x +3

• y = x + 3

• Conclusion: Therefore, the line is the graph of the linear function y = x + 3

Open Ended

Lines 1, 2, and 3 are graphs of linear functions. Find the expressions for each (page 63)

​***Slope and coordinates of a point on the graph

​***Slope and coordinates of a point on the graph

Open Ended

y is a linear function of x. The graph of the function is a line that passes through the point (1,2) and the slope of -3. Find the expression for linear function

​***Coordinates of two points on the graph

​y is a linear function of x. The graph of the function is a line that passes through point (1 , 2) and point (5 , -6). Find the expression for linear function

​***Coordinates of two points on the graph

​y is a linear function of x. The graph of the function is a line that passes through point (1 , 2) and point (5 , -6). Find the expression for linear function

​***Coordinates of two points on the graph

​y is a linear function of x. The graph of the function is a line that passes through point (1 , 2) and point (5 , -6). Find the expression for linear function

​Solution: y = mx + b ; coordinates (x , y): (1 , 2) and (5 , -6)

m (slope): - 2

Find the intercept (b)

2 = -2(1) + b

b = 2 + 2

b = 4

The expression for this linear function is y = -2x + 4

Open Ended

y is a linear function of x. The graph of the function is a line that passes through point (-1,-4) and point (3,8). Find the expression for linear function