A. The y-intercept is 11.
B. In context, the y-intercept represents the cost of the meal when no side dishes are chosen.
C. The slope is 1.25.
D. In context, the slope represents the increase in cost for each additional side dish added to the meal.
E. To find the number of side dishes Jodi got, we can substitute the cost of her meal ($18.50) into the equation and solve for x:
18.50 = 11 + 1.25x
7.50 = 1.25x
x = 6
Therefore, Jodi got 6 side dishes with her meal.
The following equation represents the cost of buying a meal with one meat and options for the number of side dishes, x. y = 11 + 1.25x (5 points)
A. what is the y-intercept
B. what does the y-intercept mean in context
C. what is the slope
D. what does the slope mean in context
E. if Jodi paid $18.50 for her meal, how many side dishes did she get
9 answers
The equation of the line is given by y = mx + b. Solve for x in terms of y. (1 point)
x = y/m + b
x = y + b/m
x = y - b/m
x = y/m - b
x = y/m + b
x = y + b/m
x = y - b/m
x = y/m - b
To solve for x in terms of y, we need to isolate x on one side of the equation.
The equation y = mx + b can be rearranged as:
y - b = mx
Now, divide both sides of the equation by m:
(y - b) / m = x
So, x = (y - b) / m.
The equation y = mx + b can be rearranged as:
y - b = mx
Now, divide both sides of the equation by m:
(y - b) / m = x
So, x = (y - b) / m.
The equation of line 1: 4x - 2y = 16
The equation of line 2: y = -4/5x + 2
The equation of line 3: y - 4 = 3 (x + 5)
Which statement is true?
Line 2 has the biggest y-intercept
Line 1 has the biggest y-intercept
Line 3 has the greatest slope
Line 3 has a decreasing graph
Line 2 has an increasing graph
Line 1 has the greatest slope
The equation of line 2: y = -4/5x + 2
The equation of line 3: y - 4 = 3 (x + 5)
Which statement is true?
Line 2 has the biggest y-intercept
Line 1 has the biggest y-intercept
Line 3 has the greatest slope
Line 3 has a decreasing graph
Line 2 has an increasing graph
Line 1 has the greatest slope
To determine which statement is true, let's analyze each option:
Line 2 has the biggest y-intercept:
The y-intercept of line 2 is 2, which means it intersects the y-axis at the point (0, 2).
Line 1 has the biggest y-intercept:
To find the y-intercept of line 1, we need to express it in slope-intercept form.
Starting with the original equation:
4x - 2y = 16
We can rearrange it to:
-2y = -4x + 16
Dividing both sides by -2:
y = 2x - 8
The y-intercept of line 1 is -8, which means it intersects the y-axis at the point (0, -8).
Line 3 has the greatest slope:
Comparing the equations, we can determine the slopes of each line:
Line 1 has a slope of 4/2, which simplifies to 2.
Line 2 has a slope of -4/5.
Line 3 has a slope of 3.
Line 3 has a decreasing graph:
The equation of line 3 is in slope-intercept form, y = 3x - 11. Since the coefficient of x (3) is positive, the line has a positive slope, which means it is increasing rather than decreasing.
Line 2 has an increasing graph:
Since the slope of Line 2 is negative (-4/5), the line has a decreasing graph, not an increasing one.
Line 1 has the greatest slope:
From earlier analysis, line 1 has a slope of 2, which is greater than the slopes of line 2 (-4/5) and line 3 (3).
Based on the analysis, the statement that is true is: Line 1 has the greatest slope.
Line 2 has the biggest y-intercept:
The y-intercept of line 2 is 2, which means it intersects the y-axis at the point (0, 2).
Line 1 has the biggest y-intercept:
To find the y-intercept of line 1, we need to express it in slope-intercept form.
Starting with the original equation:
4x - 2y = 16
We can rearrange it to:
-2y = -4x + 16
Dividing both sides by -2:
y = 2x - 8
The y-intercept of line 1 is -8, which means it intersects the y-axis at the point (0, -8).
Line 3 has the greatest slope:
Comparing the equations, we can determine the slopes of each line:
Line 1 has a slope of 4/2, which simplifies to 2.
Line 2 has a slope of -4/5.
Line 3 has a slope of 3.
Line 3 has a decreasing graph:
The equation of line 3 is in slope-intercept form, y = 3x - 11. Since the coefficient of x (3) is positive, the line has a positive slope, which means it is increasing rather than decreasing.
Line 2 has an increasing graph:
Since the slope of Line 2 is negative (-4/5), the line has a decreasing graph, not an increasing one.
Line 1 has the greatest slope:
From earlier analysis, line 1 has a slope of 2, which is greater than the slopes of line 2 (-4/5) and line 3 (3).
Based on the analysis, the statement that is true is: Line 1 has the greatest slope.
The equation 7x + 5y = 100 is in standard form.This form tells us the x and y intercept easily. What are the x and y intercepts
the line crosses the x-axis at (20, 0) and crosses the y-axis at (0, 100/7)
the line crosses the x-axis at (7/100, 0) and crosses the y-axis at (0, 1/20)
the line crosses the x-axis at (7, 0) and crosses the y-axis at (0, 5)
the line crosses the x-axis at (100/7, 0) and crosses the y-axis at (0, 20)
the line crosses the x-axis at (20, 0) and crosses the y-axis at (0, 100/7)
the line crosses the x-axis at (7/100, 0) and crosses the y-axis at (0, 1/20)
the line crosses the x-axis at (7, 0) and crosses the y-axis at (0, 5)
the line crosses the x-axis at (100/7, 0) and crosses the y-axis at (0, 20)
To find the x-intercept, we set y = 0 in the equation 7x + 5y = 100 and solve for x:
7x + 5(0) = 100
7x = 100
x = 100/7
So, the line crosses the x-axis at (100/7, 0).
To find the y-intercept, we set x = 0 in the equation 7x + 5y = 100 and solve for y:
7(0) + 5y = 100
5y = 100
y = 100/5
y = 20
So, the line crosses the y-axis at (0, 20).
Therefore, the x and y intercepts of the line are (100/7, 0) and (0, 20).
7x + 5(0) = 100
7x = 100
x = 100/7
So, the line crosses the x-axis at (100/7, 0).
To find the y-intercept, we set x = 0 in the equation 7x + 5y = 100 and solve for y:
7(0) + 5y = 100
5y = 100
y = 100/5
y = 20
So, the line crosses the y-axis at (0, 20).
Therefore, the x and y intercepts of the line are (100/7, 0) and (0, 20).
Michele has $25. She plans to save $10 per week until she has a total of $75. Which equation matches this scenario.
y = 10x - 25
y - 55 = 10 (x - 3)
10x + y = 25
y + 4 = 10 (x - 65)
y = 10x - 25
y - 55 = 10 (x - 3)
10x + y = 25
y + 4 = 10 (x - 65)
Let's analyze each equation to see which one matches the given scenario:
y = 10x - 25:
This equation represents a linear relationship with a slope of 10 and a y-intercept of -25. However, it does not match the given scenario as there is no mention of starting with -$25. Also, it does not account for the specific target of reaching $75.
y - 55 = 10 (x - 3):
This equation represents a linear relationship with a slope of 10 and a point (3, 55) on the line. It does not match the given scenario as there is no mention of starting with $55. Also, it does not account for the specific target of reaching $75.
10x + y = 25:
This equation represents a linear relationship with a slope of -10 and a y-intercept of 25. It does not match the given scenario as there is no mention of starting with $25 or saving $10 per week.
y + 4 = 10 (x - 65):
This equation represents a linear relationship with a slope of 10 and a point (65, -4) on the line. It does not match the given scenario as there is no mention of starting with -$4. Also, it does not account for the specific target of reaching $75.
None of the provided equations match the given scenario.
y = 10x - 25:
This equation represents a linear relationship with a slope of 10 and a y-intercept of -25. However, it does not match the given scenario as there is no mention of starting with -$25. Also, it does not account for the specific target of reaching $75.
y - 55 = 10 (x - 3):
This equation represents a linear relationship with a slope of 10 and a point (3, 55) on the line. It does not match the given scenario as there is no mention of starting with $55. Also, it does not account for the specific target of reaching $75.
10x + y = 25:
This equation represents a linear relationship with a slope of -10 and a y-intercept of 25. It does not match the given scenario as there is no mention of starting with $25 or saving $10 per week.
y + 4 = 10 (x - 65):
This equation represents a linear relationship with a slope of 10 and a point (65, -4) on the line. It does not match the given scenario as there is no mention of starting with -$4. Also, it does not account for the specific target of reaching $75.
None of the provided equations match the given scenario.