Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows on both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 3 comma 0 right parenthesis.
Write the equation of the line in slope-intercept form
To write the equation of the line in slope-intercept form (y = mx + b), we first need to find the slope of the line.
Slope (m) = (y2 - y1) / (x2 - x1)
Let (x1, y1) = (0, -2) and (x2, y2) = (3, 0)
m = (0 - (-2)) / (3 - 0)
m = 2 / 3
Now that we have the slope, we can use one of the points given to find the y-intercept (b).
Using the point (0, -2):
-2 = (2/3)(0) + b
-2 = b
Now we can write the equation of the line in slope-intercept form:
y = (2/3)x - 2
Jonas is saving money for an upcoming vacation. He currently has $50 in his savings account. He plans to add $3 each week. Write an equation that represents the relationship between the amount of money, y , and the number of weeks, x . Use the slope-intercept form y=mx+b .(1 point)
Given that Jonas starts with $50 and plans to add $3 each week, we can write the equation in slope-intercept form as follows:
y = 3x + 50
Where:
y = the amount of money
x = number of weeks
m = slope (3, because he adds $3 each week)
b = y-intercept (starting amount of $50)
On a field trip, one chaperone is required for every 15 students. Is this a proportional or a nonproportional situation?
Enter 1 if this is a proportional situation. Enter 2 if this is a nonproportional situation.
(1 point)
This is a proportional situation.
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 4 right parenthesis and left parenthesis 1 comma 8 right parenthesis.
Derive the equation of the line in slope-intercept form.
(1 point)
To find the equation of the line in slope-intercept form (y = mx + b), we first need to find the slope (m) of the line, using the coordinates (0, 4) and (1, 8).
slope (m) = (y2 - y1) / (x2 - x1)
Let (x1, y1) = (0, 4) and (x2, y2) = (1, 8)
m = (8 - 4) / (1 - 0)
m = 4 / 1
m = 4
Now, we can use the slope and one point from the line to find the y-intercept (b). Let's use the point (0, 4).
y = mx + b
4 = 4(0) + b
b = 4
Therefore, the equation of the line in slope-intercept form is:
y = 4x + 4