Let's analyze the points given in the graph: (0,5), (3,3), and (6,1).
a. What is the y-intercept?
The y-intercept is the point where the line crosses the y-axis. From the points provided, the y-intercept is the y-coordinate of the point (0,5), which is 5.
b. What is the slope?
The slope (m) can be calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (0,5) and (3,3):
\[ m = \frac{3 - 5}{3 - 0} = \frac{-2}{3} \]
So, the slope is -2/3.
c. What is the equation of the line in slope-intercept form?
The slope-intercept form is given by:
\[ y = mx + b \]
Where \( m \) is the slope and \( b \) is the y-intercept.
Using the slope (-2/3) and the y-intercept (5):
\[ y = -\frac{2}{3}x + 5 \]
d. This is a linear relationship.
Since the points form a straight line, the relationship between x and y is linear.
In summary:
a. 5
b. -2/3
c. y = -2/3x + 5
d. linear