Linear Graphs

Linear Graphs revision

Chapter 6

6B Determining the slope of a straight line

• Represented by "b" in the equation

• + slope rise from left to right

•  $-$  slope fall from left to right

• zero slope = straight horizontal line

• un defined slope = straight vertical line

• Divide rise by run to find slope

•  $b=\frac{y_2-\ y_1}{x_2-x_1}$  

Multiple Choice

Find the slope of the line through the points (0,10) and (4,2)

• 2

• 1

• -2

• $$-\frac{1}{2}$$

• $$\frac{1}{2}$$

6C The intercept-slope form of the equation of a straight line

• Represented by "a" in an equation

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

Multiple Choice

The y-intercept in the following equation is

$$y=10+5x$$  

• (0,10)

• (10,0)

• (0,5)

• (5,0)

• (2,0)

Multiple Choice

The y-intercept and slope of the following equation is

$$y=6-3x$$  

• y int = -6   slope = -3

• y int = -6   slope = 3

• y int = 6   slope = -3

• y int = 6   slope = 3

• y int = -3   slope = 6

6D Finding the equations of a straight-line graph from its intercept and slope

• 1) Identify the y-intercept (a)

• 2) Use two points on graph to find slope (b)

• 3) Substitute these two values into the standard equation y=a+bx

Multiple Choice

The equation of the graph is

• y=-2-1.4x

• y=2+1.4x

• y=2-1.4x

• y=-2+1.4x

• y=2+14x

6E 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 (b)

• 2) Substitute this value for the slope (b) into the equation.

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

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

Multiple Choice

The equation of the graph is

• y=8+4.5x

• y=-8-4.5x

• y=8-4.5x

• y=-8+4.5x

• y=-4.5+8x