Answer:
C: y - 1 = -2/3(x - 3)
Step-by-step explanation:
The given answer is the point-slope form of the linear equation, y = -2/3x + 3.
The point-slope form is:
y - y1 = m(x - x1)
where m = slope.
Given the two points on the graph, (0 , 3) and (3, 1), we can solve for the slope of the line by using the following formula:
[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
Let x1 = 0, x2 = 3,
y1 = 3, y2 = 1
Plug in these values into the slope formula:
[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{1 - 3}{3 - 0} = \frac{-2}{3}[/tex]
Therefore, the slope of the line is -2/3.
Next, we must identify the y-intercept (which is the y-coordinate of the point where the graph of the linear equation crosses the y-axis). This is given by point, (0, 3). Therefore, the y-intercept is 3.
Using one of the points on the graph, (3, 1), we can plug in these values into our point-slope formula:
y - y1 = m(x - x1)
y - 1 = -2/3(x - 3)
