Spiral Review (10/21-10/25)

Graph the line.

y = -2/3x + 5

Answer explanation

Your slope (rise over run) is -2/3.

The y-intercept is 5.

This means you will need to start at 5 on the y-axis, then count down 2 and right 3 to find your next point.

Graph the equation.

y - 3 = 3(x + 2)

Answer explanation

y - 3 = 3(x + 2)

There are two methods to graph this line:

Option 1

Recognize that this is point-slope form, which is y-y1=m(x-x1).

This means that m = 3, x1 = -2, and y1 = 3.

(x1, y1) tells you a point that you can plot first, then you can use m = 3 to graph your rise over run (up 3 right 1).

Option 2

Convert the equation into slope-intercept form, y=mx+b.

To do this, you would first distribute the 3, multiplying it with the x and the +2. Then you would cancel out the -3 from the left-side.

Now you would see the slope and y-intercept.

Graph the equation.

x - 4y = 8

Answer explanation

x - 4y = 8

There are two ways to graph this equation.

Option 1

Recognize that this is standard form, ax+by=c.

This means that the slope is -A/B, the x-intercept is C/A, and the y-intercept is C/B.

Option 2

Rewrite the equation to slope-intercept form, y=mx+b.

To do this, subtract the x to move it to the right hand side, then divide by the coefficient of y.

Then you would see the slope and y-intercept.

What is the RATE OF CHANGE shown in the graph?

Mathematical Equivalence

ON

Answer explanation

Remember RATE OF CHANGE is the same thing as SLOPE!

Select two points on the graph.

Then either use the slope formula OR count the rise over run.

Remember that if the line is going uphill, the slope is positive. If the slope is going downhill, the slope is negative.

What is the RATE OF CHANGE shown in the table?

Mathematical Equivalence

ON

Answer explanation

Remember RATE OF CHANGE is the same thing as SLOPE!

Select two points from the table.

Use the slope formula.

What is the equation of the line that has a slope of 1/5 and passes through the point (-5, -3)?

Answer in slope-intercept form: y=mx+b

Mathematical Equivalence

ON

Answer explanation

Use the point-slope formula y-y1=m(x-x1).

m = 1/5, x1 = -5, and y1 = -3

After replacing m, x1, and y1 with those values, simplify by changing any "minus negatives" into plus signs, distributing, and then getting y by-itself.

what is the slope of the following 12x - 6y = 30

Mathematical Equivalence

ON

What is the equation of the line that passes through the points (-4, -4) and (3, 4)?

Type your answer in slope-intercept form.

Mathematical Equivalence

ON

Answer explanation

Step 1 - use the slope formula to identify m.

Step 2 - choose one point to be the values for x1 and y1

Step 3 - use m, x1, and y1 in the point-slope formula, y-y1=m(x-x1)

Step 4 - simplify and rewrite into slope-intercept form, y=mx+b

What is the equation of the line shown in the graph?

Type your answer in slope-intercept form.

Mathematical Equivalence

ON

Answer explanation

Step 1 - identify the y-intercept. This will be your "b"

Step 2 - identify the slope. You can either use the slope formula or count the rise over run from the graph. This will be your "m"

Step 3 - use m and b in the slope-intercept formula, y=mx+b

What is the equation of the line shown in the table?

Type your answer in slope-intercept form.

Mathematical Equivalence

ON

Answer explanation

Step 1 - choose two points to use with the slope formula to determine "m"

Step 2 - use m and one of the points to plug into the point-slope formula, y-y1=m(x-x1)

Step 3 - simplify and get y by-itself