Answer:
The correct option is;
It has the same slope and a different y-intercept
Step-by-step explanation:
The data on the table can be presented as follows;
x [tex]{}[/tex] y
-2/3 [tex]{}[/tex] -3/4
-1/6 [tex]{}[/tex] -9/16
1/3 [tex]{}[/tex] -3/8
5/6 [tex]{}[/tex] -3/16
The rate of change of the function, m = (-3/16 - (-3/4))/(5/6 - (-2/3)) = 3/8
The equation of the line given by the data points in point and slope form is given as follows;
y - (-3/16) = 3/8×(x - 5/6)
y = 3·x/8 - 5/16 - 3/16 = 3·x/8 - 1/2
y = 3·x/8 - 1/2
The y intercept is given at when x = 0, therefore, at the y-intercept, y = 3 × 0/8 - 1/2 = -1/2
The y-intercept is (0, -1/2)
The x-intercept occurs at y = 0, therefore, at the x-intercept, we have;
0 = 3·x/8 - 1/2
∴ 3·x/8 = 1/2
x = 4/3
Therefore, the x-intercept is 4/3 and the coordinates of the x-intercept is (4/3, 0)
Given that the x-intercept is different, the y-intercept of the two lines with the same slope are also different
The correct option is therefore that it has the same slope and a different y-intercept;
