Linear Graphs Revision

Linear Graphs

Determining the slope of a straight line

• Represented by "m" in the linear equation

• + slope rises from left to right

•  −  slope falls from left to right

• zero slope create a straight horizontal line

• undefined slope creates a straight vertical line

• Divide rise by run to find slope

•  $m\ =\frac{y_2\ -\ y_1}{x_2\ -\ x_1}$  

Multiple Choice

Find the slope of (5 , 8) and (3, 2)

• 2

• 3

• -2

• -3

• 1/2

The slope - intercept form of the equation of a straight line

• Represented by "b" in an equation

• Shows where to line meets/cuts the y-axis (x=0)

• When a line crosses the Y- axis, the point where it cuts through is called the intercept.

Multiple Choice

The y-intercept in the following equation is

y= 2x + 7

• (7 , 0)

• (0 , 2)

• (2 , 0)

• (0 , 7)

• (-7, 0)

Multiple Choice

The y-intercept and slope of the following equation is

y=12 - 2x

• y int = -2 slope = -12

• y int = 12 slope = -2

• y int = 12 slope = 2

• y int = -12 slope = -2

• y int = -2 slope = 12

Finding the equations of a straight-line graph from its intercept and slope

• 1) Use two points on graph to find slope (m)

• 2) Identify the y-intercept (b)

• 3) Substitute these two values into the standard equation y= mx + b

Multiple Choice

The equation of the graph is

• y = 4x - 5

• y = 5 - 2x

• y = 2x + 5

• y = 3x + 5

Finding the equation of a straight-line graph using to points on the graph

• 1) Use the coordinates of two points to determine the slope (m)

• 2) Substitute this value for the slope (m) into the equation y = mx + b

• 3) Substitute the coordinates of one of the two points on the line into this new equation and solve for the unknown (b)

• 4) Substitute the values of m and b into the general equation y=mx + b to obtain the equation of the straight line

Multiple Choice

The equation of the graph is

• $y\ =\ \frac{1}{\text{4}}x\ -\ 2$
  

• $y\ =\ -\frac{1}{\text{4}}x\ +\ 2$

• $y\ =\ -\frac{1}{\text{4}}x\ -\ 2$

• $y\ =\ \frac{1}{\text{4}}x\ +\ 2$

Multiple Choice

The equation of the graph is

• $y\ =\ \frac{1}{\text{4}}x\ -\ 2$
  

• $y\ =\ -\frac{1}{\text{4}}x\ +\ 2$

• $y\ =\ -\frac{1}{\text{4}}x\ -\ 2$

• $y\ =\ \frac{1}{\text{4}}x\ +\ 2$