The outputs and inputs to form the coordinate pairs that fit onto the straight line represented by the function y = (2/3)·x + 5 are;
B. When the input is 0, the output is 5
D. An output of 6 results from an input of 3/2
E. An output of 4 results from an input of -3/2
What is the equation of a straight line; The equation of a straight line in slope-intercept form is; y = m·x + b, where m is the slope of the graph of the line and b is the y-intercept.
The outputs for the linear function y = (2/3)·x + 5 for the inputs, x = 1, 0, and 5 are;
When x = 1, y = (2/3) × 1 + 5
y = (2/3) + 5
(2/3) + 5 = 17/3
When x = 0, y = (2/3) × 0 + 5
y = 0 + 5
y = 5
The option B is correct
When x = 5, y = (2/3) × 5 + 5
y = (10/3) + 5
(10/3) + 5 = 25/3
The inputs for the function y = (2/3)·x + 5 for the outputs, y = 6, 4, and 2 are;
y = (2/3)·x + 5
x = (y - 5) × (3/2)
When y = 6, x = (6 - 5) × (3/2)
(6 - 5) × (3/2) = 3/2
x = 3/2
The option D is correct
When y = 4, x = (4 - 5) × (3/2)
(4 - 5) × (3/2) = -3/2
x = -3/2
The option E is correct
When y = 2, x = (2 - 5) × (3/2)
(2 - 5) × (3/2) = -9/2
x = -9/2
Therefore, options B, D, and E are points that form coordinate pairs on the straight line of the function