An illustration shows a coordinate plane with 4 quadrants. The x-axis ranges from negative 9 to 9 in one unit increments, and the y-axis ranges from negative 11 to 11 in one unit increments. A line is graphed on the plane. An upward slanting line line passes through points plotted at left parenthesis 3 comma 3 right parenthesis and left parenthesis 8 comma 8 right parenthesis.
Use the graph to derive the equation y=mx for a line through the origin. Simplify the numerical coefficient, if needed.
(1 point)
Responses
y=3x
y equals 3 x
y=8x
y equals 8 x
y=x
y equals x
y=3/3x
y equals 3/3 x
An illustration shows a graph labeled Inches per Feet. The horizontal axis is labeled feet and ranges from 0 to 4 in increments of 1. The vertical axis is labeled Inches and ranges from 0 to 40 in increments of 4. An upward slanting line segment connects points plotted at left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 12 right parenthesis, left parenthesis 2 comma 24 right parenthesis, and left parenthesis 3 comma 36 right parenthesis.
The proportional relationship between inches and feet is displayed on the graph. Derive the equation of the line through the origin.
(1 point)
Responses
y=12x
y equals 12 x
y=2x
y equals 2 x
y=1/12x
y equals Start Fraction 1 over 12 End Fraction x
y=36x
y equals 12 x
Use the table to answer the question.
x y (x, y)
0 (0, )
1 (1, )
2 (2, )
Complete the ordered pairs in the table by finding the y-value of the ordered pairs for the equation y=5x.
(1 point)
Responses
(0, 0), (1, 15) , (2, 25)
left parenthesis 0 comma 0 right parenthesis , left parenthesis 1 comma Start Fraction 1 over 5 End Fraction right parenthesis , left parenthesis 2 comma Start Fraction 2 over 5 End Fraction right parenthesis
(0, 0), (1, 5), (3, 15)
left parenthesis 0 comma 0 right parenthesis , left parenthesis 1 comma 5 right parenthesis , left parenthesis 3 comma 15 right parenthesis
(0, 0), (1, 5), (2, 10)
left parenthesis 0 comma 0 right parenthesis , left parenthesis 1 comma 5 right parenthesis , left parenthesis 2 comma 10 right parenthesis
(0, 0), (5, 1), (10, 2)
(0, 0), (1, 5), (2, 10)
A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins two plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis and left parenthesis 5 comma 1 right parenthesis.
Is this the correct graph of the equation y=15x?
(1 point)
Responses
Yes, it is the correct graph because the ordered pair (0, 0) satisfies the equation and the slope m=riserun=15.
Yes, it is the correct graph because the ordered pair left parenthesis 0 comma 0 right parenthesis satisfies the equation and the slope m equals Start Fraction rise over run End Fraction equals Start Fraction 1 over 5 End Fraction .
No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of y=15x
No, it is not the correct graph because the ordered pair left parenthesis 1 comma 5 right parenthesis is not a point on the graph of y equals Start Fraction 1 over 5 End Fraction x
Yes, it is the correct graph because the slope =51.
Yes, it is the correct graph because the slope equals Start Fraction 5 over 1 End Fraction .
No, it is not the correct graph because the slope m=riserun=15.
No, it is not the correct graph because the slope m=15, which means the line should be steeper.
Given the table for x, time in minutes and y, distance traveled:
x - time 4 3 10 7 9
y - distance 76 57 190 133 171
(4 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
a. Every minute __ meters are traveled.
b. Write an equation to show the relationship between x and y. Response area
c. This relationship is because the y-intercept is Response area .
a. Every minute 19 meters are traveled.
b. Write an equation to show the relationship between x and y. Response area
We can see that there is a linear relationship between x (time) and y (distance), so we can write the equation as y = mx + b, where m is the slope and b is the y-intercept. To find the equation, we can use two of the given points to find the slope:
Using the points (4, 76) and (3, 57), we can calculate the slope:
m = (y2 - y1) / (x2 - x1)
= (57 - 76) / (3 - 4)
= -19
So the equation is y = -19x + b.
c. This relationship is because the y-intercept is Response area.
To find the y-intercept, we can substitute one of the points into the equation and solve for b. Let's use the point (4, 76):
76 = -19(4) + b
76 = -76 + b
b = 152
So the equation is y = -19x + 152 and the relationship is linear because the y-intercept is 152.
Solve this equation for y: y/3=2x
(1 point)
Responses
y=2x+3
y is equal to 2 x plus 3
y=6x
y is equal to 6 x
y=2/3x
y is equal to 2 thirds x
y=2x−3