8.5B-Non-Proportional Linear Relationships

Which linear function best describes the graph above?

• y=3/5x+4

• y=5/3x+4

• y=3/5x-6.5

• y=5/3x+6.5

Answer explanation

We can see that the y-intercept (b) is 4. From there, using rise/run, we can see that we go up 3 and over 5, making the slope 3/5. Substituted into the equation y=mx+b, we would have the equation y=3/5x+4.

What is the y-intercept of this graph?

• (0, 4)

• (0,-2)

• (0,-4)

• (-4,0)

Answer explanation

We know that the x-value for the y-intercept will ALWAYS be 0 and it passes through the y-axis at -4, making the coordinate (0,-4).

What is the slope of the line in the graph?

• m=-2

• m=-1/2

• m=2

• m=-4

Answer explanation

We know, based on the direction of the line, that the slope is negative. We can use rise/run and we see that we go down 2 (the negative movement) and over 1. m=-2/1=-2.

The slope of the line in the graph is negative.

• True

• False

Answer explanation

The slope of the line is negative. As we travel to the right the x values are increasing and the y-values are decreasing.

What is the y-intercept of the graph?

• b=-2

• b=-1

• b=1

• b=-1/2

Answer explanation

The y-intercept is -1. The y-intercept is the point on the graph where the line of the graph crosses the y-intercept.

What linear function best describes this graph?

• y=-1/2x+1

• y=1/2x-1

• y=-1/2x-1

• y=-2x+1

Answer explanation

We have identified the y-intercept (b) as -1. We know that we have a negative slope and using rise/run we see that we go down one and over 2, making the slope -1/2. Substituting these values into the equation we get y=-1/2x-1.

What is the y-intercept of the graph?

• b=2

• b=8

• b=1/4

• b=-2

Answer explanation

The line of the graph passes through the y-axis at the point (0,-2).

What is the slope of the line of the graph?

• m=-1/4

• m=-2

• m=1/4

• m=8

Answer explanation

Using rise/run, we can see that we go up one and over 4, making our slope 1/4. Remember, slopes that are less than one are going to be flatter.

What is the equation of the function represented by the graph?

• y=1/4x-2

• y=-1/4x-2

• y=1/4x+2

• y=4x+8

Answer explanation

We can see that the y-intercept (b) is -2 and the slope of the graph (m) is 1/4. When we substitute these values into the equation y=mx+b we get y=1/4x-2.

What is the equation of the line in the graph ?

• y=-1/2x+5

• y=1/2x+5

• y=1/2x-5

• y=-1/2x+10

Answer explanation

We can see that the y-intercept is 5 and that the slope is negative. Using the slope formula (y2-y1)/(x2-x1) we can substitute in the values (2-4)/(6-2). This simplifies to -2/4, which reduces to -1/2.