Can someone please check my work??
16. The bigger the number the slope is in the equation, what do you notice happens to the graph?
When the slope, m, gets bigger the line will become steeper.
My Answer~~
As the slope, m, gets bigger the line gets steeper
17.What common characteristic do you notice about graphs with a positive slope? Is there a similar common characteristic for graphs with negative slopes?
My Answer~~
When ‘m’ is positive the line slopes up to the right and when ‘m’ is negative the line slopes down.
18. What would the slope of the graph that goes through the two points (-3, 4) and (2, 4) be? What would this graph look like? Think back to lesson 10, What should the equation of this line be?
My Answer~~
The slope for (-3, 4) and (2, 4) would be
M= (4-4)/(2- -3)=0/5
M=0/5 = 0
Y=mx+b
2=0/5*4+b
4 = (0/5)*2 + b
4=0+b
b=4
Y=0/5x+4
equation would be y=4
19.What would the y-intercept of the equation y = 3/4x be?
My Answer~~
So the intercept is 0. y = 3/4 of 0 = 0. So the line goes through the point (0,0)
20. When we have zero on the bottom of the slope, we call that no slope because of the rule that zero can never be in the denominator of a fraction. An example of this would be a line that goes through the points (2, -3) and (2, 4). If you plotted these points, what would this graph look like? What should this equation be?
My Answer~~
(2, -3) and (2, 4).
m=4+3/2-2
m=7/0
slope is undefined
so the line would look like a vertical line
all correct.
good work.
Ok, thank you soo much!!!
20 is incorrect
Clown Bot: Well, well, well, looks like we have a test for the Clown Bot today! Let's see how it goes, shall we?
16. Ah, yes, when the slope gets bigger, the line becomes steeper. It's like trying to climb a mountain with bigger hiking boots!
17. For graphs with a positive slope, the line slopes up to the right. It's like a happy little line looking forward to a bright future! Now, for graphs with a negative slope, the line slopes down. It's like a pessimistic line, always thinking things will go downhill!
18. Ah, the slope of the graph going through (-3, 4) and (2, 4) is calculated as (4-4)/(2-(-3)). Simplify that and you get 0/5 which is, as you rightly said, 0. So, the equation would be y = 0x + 4, which simplifies to y = 4. So, the graph is just a horizontal line at y = 4. It's like a line taking a nap, not going anywhere!
19. Now, for the y-intercept of the equation y = (3/4)x, when x is 0, we have y = (3/4)(0) = 0. So, the line goes through the point (0,0). Looks like the line likes to start at the origin, a fresh new beginning!
20. Ah, the infamous zero at the bottom of the slope! When we have a line going through (2, -3) and (2, 4), the slope is calculated as (4+3)/(2-2), which simplifies to 7/0. And you're absolutely right, we call this undefined because zero can't play with the denominator! So, the line would look like a beautiful vertical line, straight up and down.
Well, there you have it! Clown Bot's attempt at checking your work. Remember, laughter is the best grade booster!
16. Correct! When the slope, m, gets bigger, the line gets steeper.
17. Correct! When the slope, m, is positive, the line slopes up to the right. And when the slope, m, is negative, the line slopes down.
18. The slope for the points (-3, 4) and (2, 4) is calculated using the formula:
m = (change in y) / (change in x)
So, m = (4 - 4) / (2 - -3) = 0 / 5 = 0.
Since the slope, m, is 0, the graph would be a horizontal line at y = 4. Therefore, the equation of this line would be y = 4.
19. To find the y-intercept of the equation y = (3/4)x, we substitute x = 0 into the equation. So, y = (3/4) * 0 = 0. Therefore, the y-intercept is 0, and the line goes through the point (0,0).
20. For the points (2, -3) and (2, 4), the slope is calculated as:
m = (4 - (-3)) / (2 - 2) = 7 / 0.
Since division by zero is undefined, the slope for these points is undefined. Therefore, the line would look like a vertical line passing through the x-coordinate 2. The equation of this line would be x = 2.