whats the slope for y=−3x+2
The slope of a linear equation in the form y = mx + b is represented by the coefficient of x, which is m.
In the equation y = -3x + 2, the slope (m) is -3.
which one of these match this equation
Cynthia has $200 in her savings account and spends $3 per day on coffee. or James increases his muscle mass by 3 kg per day.
The equation y = -3x + 2 represents the relationship between the variables y and x, where y represents the value of something and x represents the number of a specific time or quantity.
Out of the given options, the equation "James increases his muscle mass by 3 kg per day" does not match the equation y = -3x + 2.
so its Cynthia has $200 in her savings account and spends $3 per day on coffee.
Yes, the equation y = -3x + 2 matches the scenario "Cynthia has $200 in her savings account and spends $3 per day on coffee". In this equation, y represents the amount of money remaining in Cynthia's savings account after x days, and the slope (-3) represents the rate at which her savings decrease by $3 per day. The constant term (2) represents her initial savings of $200.
The equation of Line 1: 2x−4y=16
The equation of Line 2: y=−34x−3
The equation of Line 3: y−5=−2(x+1)
Which statement is true?
(2 points)
Responses
Line 3 has the least steep slope.
Line 2 has an increasing graph.
Line 1 has the steepest slope.
Line 1 has the biggest y-intercept.
Line 2 has the biggest y-intercept.
Line 3 has a decreasing graph.
To determine which statement is true, we'll analyze the given equations:
Line 1: 2x - 4y = 16
Rearranging this equation in slope-intercept form (y = mx + b), we get:
-4y = -2x + 16
y = (1/2)x - 4
The slope of Line 1 is 1/2, so it does not have the steepest slope.
Line 2: y = -34x - 3
The slope of Line 2 is -34. However, since it's negative, Line 2 has a decreasing graph.
Line 3: y - 5 = -2(x + 1)
y - 5 = -2x - 2
y = -2x + 3
The slope of Line 3 is -2.
Comparing the slopes of the three lines, we find that Line 2 (-34) has the least steep slope.
Comparing the y-intercepts:
Line 1 is in the form y = (1/2)x - 4, so its y-intercept is -4.
Line 2 is in the form y = -34x - 3, so its y-intercept is -3.
Line 3 is in the form y = -2x + 3, so its y-intercept is 3.
Therefore, Line 3 has the biggest y-intercept.
In summary, the true statement is:
Line 3 has the biggest y-intercept.
The equation of Line 1: 2x−4y=16
The equation of Line 2: y=−34x−3
The equation of Line 3: y−5=−2(x+1)
Which statement is true?
(2 points)
Responses
Line 3 has the least steep slope.
Line 2 has an increasing graph.
Line 3 has a decreasing graph.
To determine which statement is true, we'll analyze the given equations:
Line 1: 2x - 4y = 16
Rearranging this equation in slope-intercept form (y = mx + b), we get:
-4y = -2x + 16
y = (1/2)x - 4
The slope of Line 1 is 1/2.
Line 2: y = -34x - 3
The slope of Line 2 is -34. However, since it's negative, Line 2 has a decreasing graph.
Line 3: y - 5 = -2(x + 1)
y - 5 = -2x - 2
y = -2x + 3
The slope of Line 3 is -2.
Comparing the slopes of the three lines, we find that Line 3 (-2) has the least steep slope.
Comparing the graphs:
Line 1 has a positive slope (1/2), which indicates an increasing graph.
Line 2 has a negative slope (-34), which indicates a decreasing graph.
Line 3 has a negative slope (-2), which also indicates a decreasing graph.
Therefore, the true statement is:
Line 3 has a decreasing graph.
Ryan is tracking how much money he has each week.
He started with $50.
He saves $15 per week for the first 6 weeks.
He spent $10 per week after week 6 until the money's all spent.
(4 points)
1) The graph of this scenario would be
because the rate of change changes.
2) The y-intercept of this graph would be
meaning
.
3) The rate of change is
after the first 6 weeks because as the weeks increase the money decreases.
1) The graph of this scenario would be a straight line with a slope of -10 after the first 6 weeks, as the money decreases at a constant rate of $10 per week.
2) The y-intercept of this graph would be $50, meaning that initially, Ryan starts with $50.
3) The rate of change is -10 after the first 6 weeks because as the weeks increase, the money decreases by $10 per week.
The equation 10x+3y=90
is in standard form. This form tells us the x and y-intercepts easily.
What are the x and y-intercepts?
(1 point)
Responses
The x-intercept is (10,0) and the y-intercept is at (0,3).
The x-intercept is (10,0) and the y-intercept is at (0,3).
The x-intercept is (1/9,0) and the y-intercept is at (0,1/30).
The x-intercept is (1/9,0) and the y-intercept is at (0,1/30).
The x-intercept is (3,0) and the y-intercept is at (0,10).
The x-intercept is (3,0) and the y-intercept is at (0,10).
The x-intercept is (9,0) and the y-intercept is at (0,30).
To find the x-intercept, we set y to 0 in the equation 10x + 3y = 90 and solve for x:
10x + 3(0) = 90
10x = 90
x = 9
Therefore, the x-intercept is (9, 0).
To find the y-intercept, we set x to 0 in the equation 10x + 3y = 90 and solve for y:
10(0) + 3y = 90
3y = 90
y = 30
Therefore, the y-intercept is (0, 30).
The correct response is:
The x-intercept is (9,0) and the y-intercept is at (0,30).
Michele has $55 after 2 weeks of saving money. She plans to have $105 after 7 weeks of saving.
Which equation matches this scenario?
(1 point)
Responses
y−55=10(x−2)
y minus 55 is equal to 10 times open paren x minus 2 close paren
y=7x+55
y is equal to 7 x plus 55
10x+7y=55
10 x plus 7 y is equal to 55
y+7=10(x+2)
To determine which equation matches the given scenario, we need to find an equation that represents the relationship between the amount of money (y) and the number of weeks (x) Michele has been saving.
Given that Michele has $55 after 2 weeks of saving and plans to have $105 after 7 weeks of saving, we can see that her savings increase by $10 per week.
Out of the provided options, the equation that matches this scenario is:
y - 55 = 10(x - 2)
This equation represents that Michele currently has $55 (the y-intercept) and her savings increase by $10 per week (the rate of change).
Therefore, the correct equation is:
y - 55 = 10(x - 2).
Using the table of values:
x cups of milk 2, 4, 5, 30
y tbl chocolate syrup 1, 2, 2.5, 15
(3 points)
1) What is the slope in context?
2) What is the y-intercept in context?
3) What is the equation of the line?
To find the slope and y-intercept in context, we can use the given table of values:
x (cups of milk): 2, 4, 5, 30
y (tablespoons of chocolate syrup): 1, 2, 2.5, 15
1) The slope in context represents the rate of change of tablespoons of chocolate syrup per cup of milk. To find the slope, we can choose any two points from the table and apply the formula:
Slope = (change in y) / (change in x)
Let's use the points (2, 1) and (30, 15):
Slope = (15 - 1) / (30 - 2)
Slope = 14 / 28
Slope = 0.5
So, in context, the slope represents that for each additional cup of milk, there is an increase of 0.5 tablespoons of chocolate syrup.
2) The y-intercept in context represents the starting amount of tablespoons of chocolate syrup, which means the value of y when x is 0. Looking at the table, we see that when x is 0, there is no entry for y. We cannot determine the y-intercept from the given data.
3) With the given data, we cannot determine the equation of the line since we do not have the y-intercept. However, if we assumed a y-intercept of 0, we can find the equation of the line using the slope-intercept form (y = mx + b). With a slope of 0.5 and a y-intercept of 0 (assumed):
y = 0.5x
Please note that this equation assumes a y-intercept of 0, which may not be accurate based on the information provided.
for 1) What is the slope in context? and 2) What is the y-intercept in context?
the answers are
No cups of milk, no syrup or 1 tbl syrup to 2 cups of milk
I apologize for the confusion in my previous response. Based on the given table of values:
x (cups of milk): 2, 4, 5, 30
y (tablespoons of chocolate syrup): 1, 2, 2.5, 15
1) The slope in context represents the rate of change of tablespoons of chocolate syrup per cup of milk. To find the slope, we can use any two points from the table and apply the formula:
Slope = (change in y) / (change in x)
Considering the points (2, 1) and (30, 15):
Slope = (15 - 1) / (30 - 2)
Slope = 14 / 28
Slope = 0.5
The slope in context indicates that for every 2 cups of milk, there is 1 tablespoon of chocolate syrup.
2) The y-intercept in context represents the starting amount of tablespoons of chocolate syrup when no cups of milk are used. From the given table, when x is 0, there is no corresponding entry for y. Therefore, we do not have enough information to determine the y-intercept in this context.
Apologies for any confusion earlier, and thank you for pointing out the corrections.