LMS-2241 Script (English)

Linear Functions and Graphs — Slope and y-intercept · Grade 8 math · Voice: en-US-AvaNeural (Microsoft Edge neural TTS, rate -6%)

Subtitle text (as shown) and the TTS input (written for pronunciation, e.g. "A" for the variable a) are both listed. Timestamps match the final video.

1. Introduction (`intro`)

Time	Subtitle	TTS input
0:05	Hi everyone! Today we're learning about linear functions and their graphs.	Hi everyone! Today we're learning about linear functions, and their graphs.
0:10	We'll focus on the two things that shape a graph: the slope and the y-intercept.	We'll focus on the two things that shape a graph: the slope, and the y-intercept.

2. What is a linear function? (`definition`)

Time	Subtitle	TTS input
0:16	First, let's see what a linear function is.	First, let's see what a linear function is.
0:20	When y can be written as a first-degree expression in x, y = ax + b, we call it a linear function of x.	When y can be written as a first-degree expression in x, y equals A x plus B, we call it a linear function of x.
0:29	But a can't be 0. If a were 0, the x term would disappear.	But A can't be zero. If A were zero, the x term would disappear.

3. Example: water tank (`example`)

Time	Subtitle	TTS input
0:35	Let's try an example. A tank holds 1 L of water, and we add 2 L every minute.	Let's try an example. A tank holds one liter of water, and we add two liters every minute.
0:42	If y is the amount of water in liters after x minutes, then y = 2x + 1.	If y is the amount of water in liters after x minutes, then y equals 2 x plus 1.
0:49	Plug in x = 0, 1, 2, and 3, and y becomes 1, 3, 5, and 7.	Plug in x equals 0, 1, 2, and 3, and y becomes 1, 3, 5, and 7.

4. Drawing the graph (`graph`)

Time	Subtitle	TTS input
0:59	Now let's plot these ordered pairs on the coordinate plane.	Now let's plot these ordered pairs on the coordinate plane.
1:03	See how the points line up? If we let x be any number, the graph of y = 2x + 1 becomes one straight line.	See how the points line up? If we let x be any number, the graph of y equals 2 x plus 1 becomes one straight line.
1:12	The graph of a linear function is always a straight line.	The graph of a linear function is always a straight line.

5. y-intercept (`intercept`)

Time	Subtitle	TTS input
1:16	Look where the line crosses the y-axis. It's the point (0, 1).	Look where the line crosses the y-axis. It's the point zero, one.
1:22	The y-coordinate of the point where a graph crosses the y-axis is called the y-intercept.	The y-coordinate of the point where a graph crosses the y-axis is called the y-intercept.
1:28	Plug in x = 0 and you get y = b, so the y-intercept of y = ax + b is b. Here, it's 1.	Plug in x equals zero, and you get y equals B. So the y-intercept of y equals A x plus B is B. Here, it's one.

6. Slope (`slope`)

Time	Subtitle	TTS input
1:38	Next is the slope. Let's see how much y increases as x increases.	Next is the slope. Let's see how much y increases as x increases.
1:44	When x goes from 0 to 1, increasing by 1, y goes from 1 to 3, increasing by 2.	When x goes from zero to one, increasing by one, y goes from one to three, increasing by two.
1:51	When x goes from 1 to 3, increasing by 2, y goes from 3 to 7, increasing by 4.	When x goes from one to three, increasing by two, y goes from three to seven, increasing by four.
2:00	Pick any two points, and the change in y divided by the change in x is always 2.	Pick any two points, and the change in y, divided by the change in x, is always two.
2:06	This constant value is called the slope. In y = ax + b, the slope is a, the coefficient of x.	This constant value is called the slope. In y equals A x plus B, the slope is A, the coefficient of x.

7. Sign of the slope (`sign`)

Time	Subtitle	TTS input
2:15	The sign of the slope tells you the direction of the graph.	The sign of the slope tells you the direction of the graph.
2:19	If a > 0, y increases as x increases, so the graph rises to the right.	If A is greater than zero, y increases as x increases, so the graph rises to the right.
2:26	If a < 0, y decreases as x increases, so the graph falls to the right.	If A is less than zero, y decreases as x increases, so the graph falls to the right.
2:33	And the larger the absolute value of a, the steeper the graph, and the closer it gets to the y-axis.	And the larger the absolute value of A, the steeper the graph, and the closer it gets to the y-axis.

8. Practice problem (`practice`)

Time	Subtitle	TTS input
2:41	Let's try a problem. Find the slope and y-intercept of y = −2x + 4.	Let's try a problem. Find the slope and y-intercept of y equals negative 2 x plus 4.
2:48	The slope is the coefficient of x, −2, and the y-intercept is the constant term, 4.	The slope is the coefficient of x, negative two, and the y-intercept is the constant term, four.
2:55	To draw the graph, first plot the y-intercept, the point (0, 4).	To draw the graph, first plot the y-intercept, the point zero, four.
3:01	Since the slope is −2, when x increases by 1, y decreases by 2. Plot (1, 2) and connect the two points. Done!	Since the slope is negative two, when x increases by one, y decreases by two. Plot the point one, two, and connect the two points. Done!
3:13	Because the slope is negative, you can see the graph falls to the right.	Because the slope is negative, you can see the graph falls to the right.

9. Summary (`summary`)

Time	Subtitle	TTS input
3:18	Let's review what we learned today.	Let's review what we learned today.
3:20	The graph of the linear function y = ax + b is a straight line. a is the slope, and b is the y-intercept.	The graph of the linear function y equals A x plus B is a straight line. A is the slope, and B is the y-intercept.
3:29	The slope is the change in y divided by the change in x, and its sign tells you the direction of the graph.	The slope is the change in y divided by the change in x, and its sign tells you the direction of the graph.
3:36	Next time, we'll use the slope and y-intercept to find the equation of a linear function. Great work today!	Next time, we'll use the slope and y-intercept to find the equation of a linear function. Great work today!

Total: 3:51 (4 s intro + 3:42 lesson + 5 s outro)

LMS-2241 Script (English)

1. Introduction (intro)

2. What is a linear function? (definition)

3. Example: water tank (example)

4. Drawing the graph (graph)

5. y-intercept (intercept)

6. Slope (slope)

7. Sign of the slope (sign)

8. Practice problem (practice)

9. Summary (summary)