Slope and Systems

Yay!!

Systems Practice!

Let's convert to slope-intercept form


2y = x - 5

Let's convert from standard to slope-intercept form

-3x + 6y = -15

Multiple Choice

What is the first step to convert this equation into slope-intercept (y=mx+b) form?

8x - 2y = 22

• Subtract 8x from both sides

• Subtract 2y from both sides

• Divide by 8

• Divide by -2

Multiple Choice

What is the correct way to subtract 8x from both sides?

8x - 2y = 22

• -2y = 14x

• -2y = 12x

• -2y = 22 - 8x

• -2y = 12 - 8x

Multiple Choice

What is the next step to convert the equation into slope-intercept (y=mx+b) form?

-2y = 22 - 8x

• Divide by -8

• Divide by -2

• Multiply by -2

• Multiply by -8

Multiple Choice

After you divide this equation by -2, what will it become?

-2y = 22 - 8x

• -y = -11 -4x

• y = -11 + 4x

• -y = -11 + 4x

• y = -11 - 4x

Math Response

What is the y-intercept of this equation?

y = -11 + 4x

Type answer here

Correct Answer: -11

Deg^°

Rad

Math Response

What is the slope of this equation?

y = -11 + 4x

Type answer here

Correct Answer: 4

Deg^°

Rad

Multiple Choice

If the slope is 4, what does that mean for how we would graph it?

• Starting at the y-intercept, go up 4 and left 1

• Starting at the y-intercept, go down 4 and left 1

• Starting at the y-intercept, go up 4 and right 1

• Starting at the y-intercept, go down 4 and right 1

Graphing

Please graph this equation:

y = -8 + 4x

(Note: this is a different equation from the one we've been using because the previous one doesn't fit on this graph)

Which of these are solutions for
-8y > 32x -8?

(0, 0)
(1, -3)
(-2, 10)

Multiple Choice

What is 4y < 16x - 4 in slope-intercept form?

• y < 4x - 1

• y > 4x - 1

• y < 4x + 1

• y > 4x +1

Multiple Select

Now that we have the inequality y < 4x - 1, which of these points are solutions to the inequality?

• (0, -1)

• (1, 4)

• (0, -2)

• (1, -4)

Hotspot

Where is the y-intercept of the red line?

Hotspot

Where is the zero of the red line?

Hotspot

Where is the y-intercept of the blue line?

Hotspot

Where is the zero of the blue line?

Drag and Drop

Let's find the rate of change with respect to x (slope) of the blue line. Remember, slope is the change in y (rise) divided by the change in x (run). For the blue line, the change in y (rise, or how much it goes up between points) is​ ​

Placeholder

and the change in x (run, or how much it moves to the right between points) is​

Placeholder

. So, the total rate of change with respect to x (slope, change in y divided by change in x) is​

Placeholder

.

Drag these tiles and drop them in the correct blank above

2

1

5

-0.5

-2

-1

-5

7

-7

0.5

Drag and Drop

Let's find the rate of change with respect to x (slope) of the red line. Remember, slope is the change in y (rise) divided by the change in x (run). For the red line, the change in y (rise, or how much it goes up between points) is​ ​

Placeholder

and the change in x (run, or how much it moves to the right between points) is​

Placeholder

. So, the total rate of change with respect to x (slope, change in y divided by change in x) is​

Placeholder

.

Drag these tiles and drop them in the correct blank above

2

1

5

-0.5

-2

-1

-5

7

-7

0.5

Open Ended

If the slope of the blue line is 2 and its y-intercept is 1, please write the equation of the blue line.

Open Ended

If the slope of the red line is -1 and its y-intercept is 7, please write the equation of the blue line.

Hotspot

Where is the solution of this system of equations?

Math Response

We can find slope from a table, too. Just like with a graph, we'll look for the change in y and the change in x. If x is the time in hours, what is the change in x between the first two points?

Type answer here

Correct Answer: 1

Deg^°

Rad

Math Response

If y is the number of meals packed, what is the change in y between the first two points?

Type answer here

Correct Answer: 125

Deg^°

Rad

Math Response

If slope is the change in y (125, the number of meals packed) divided by the change in x (1, the number of hours), what is the rate of change with respect to x (slope) shown in the table?

Type answer here

Correct Answer: 125

Deg^°

Rad

Math Response

In the last question, we found the rate of change with respect to x between the first two points (rows). Now let's look at the last two rows. What is the rate of change with respect to x (slope) shown for these two points (4, 500) and (8, 1000)?

Remember, slope is still *change in y* divided by *change in x*.

Type answer here

Correct Answer: 125

Deg^°

Rad