Question

Can someone just please help me with this ?

Question 6(Multiple Choice Worth 2 points)
(Graphing Linear Equations MC)

There is a linear relationship between the number of roses blooming in the garden and the number of days that pass. After 2 days, there are 30 rose blooms left, and after 6 days, there are 18 rose blooms left.

Which of the following graphs represents the relationship?

a coordinate plane with the x-axis labeled time in days and the y-axis labeled number of roses blooming, with a line segment that passes through the points 0 comma 34 and 8 comma 10
a coordinate plane with the x-axis labeled time in days and the y-axis labeled number of roses blooming, with a line segment that passes through the points 0 comma 36 and 8 comma 12
a coordinate plane with the x-axis labeled time in days and the y-axis labeled number of roses blooming, with a line segment that passes through the points 0 comma 38 and 8 comma 14
a coordinate plane with the x-axis labeled time in days and the y-axis labeled number of roses blooming, with a line segment that passes through the points 0 comma 40 and 8 comma 16

Answer 1

To find the correct graph that represents the linear relationship between the number of roses blooming and the number of days that pass, we need to determine the slope-intercept form of the equation of the line.

Let x be the number of days that pass and y be the number of roses blooming. We can use the two given points to find the slope:

slope = (y2 - y1)/(x2 - x1) = (18 - 30)/(6 - 2) = -3

The slope of the line is -3. To find the y-intercept, we can use one of the points and substitute the slope and x-value:

y = mx + b

30 = (-3)(2) + b

b = 36

The y-intercept of the line is 36. Therefore, the equation of the line is:

y = -3x + 36

Now we can look at the given graphs and choose the one that fits the equation. We can see that the correct graph is:

a coordinate plane with the x-axis labeled time in days and the y-axis labeled number of roses blooming, with a line segment that passes through the points 0 comma 36 and 8 comma 12.

This is because the line segment passes through the two points (0, 36) and (8, 12), which corresponds to the y-intercept and another point on the line.