Answer:
C. y = 1/3x + 4
Explanation:
To find the equation of the line that passes through the given points, we can use the slope-intercept form of the equation of a line, which is:
y = mx + b
where m is the slope of the line and b is the y-intercept.
To find the slope of the line, we can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are any two points on the line. We can choose the points (x1,y1) = (-3,3) and (x2,y2) = (6,6) from the table.
m = (6 - 3) / (6 - (-3)) = 3/9 = 1/3
Now that we have the slope, we can use the point-slope form of the equation of a line to find the y-intercept:
y - y1 = m(x - x1)
where (x1,y1) is any point on the line. We can choose the point (x1,y1) = (3,5) from the table.
y - 5 = (1/3)(x - 3)
Now we can solve for y to get the equation in slope-intercept form:
y = (1/3)x + (5 - 1/3*3)
y = (1/3)x + 4
Therefore, the equation of the line that passes through the given points is C) y= 1/3x + 4.