Question

Which equation represents the same line as the points in the table?

Input(x) -4, 0, 8/3
Output(y) 5, 2, 0

y=−3x+2
y is equal to negative 3 x plus 2

y=2x−34
y is equal to 2 x minus 3 fourths

y=−34x+83
y is equal to negative 3 fourths x plus 8 thirds

y=−34x+2

Answer 1

After testing each provided equation with the points from the table, it is determined that the equation representing the line through the given points is y = -3/4x + 2.

Step-by-step explanation:

The question asks which equation represents the line that passes through the given points. We can test each of the provided equations with the points from the table to determine the correct equation. Let's substitute the given x and y values into each equation to see if they satisfy it:

• For the first point (-4, 5), if we substitute these values into y = -3x + 2, we get 5 = -3(-4) + 2, which simplifies to 5 = 12 + 2, or 5 = 14. This is not true, so this equation does not represent the given points.
• Testing the next equation, y = 2x - 3/4, with the point (0, 2), we get 2 = 2(0) - 3/4, which simplifies to 2 = 0 - 3/4 or simply 2 != -3/4, proving that this equation also does not match the given points.
• The third equation y = -3/4x + 8/3, with the point (8/3, 0), if we substitute these values, we get 0 = -3/4(8/3) + 8/3, which simplifies to 0 = -2 + 8/3, or 0 = -6/3 + 8/3, which becomes 0 = 2/3. This is also false.
• Finally, substituting the point (0, 2) into the last equation, y = -3/4x + 2, gives us 2 = -3/4(0) + 2, which simplifies to 2 = 0 + 2 or simply 2 = 2. This is true; hence, we need to test the remaining points.

After checking all the points against all the equations, we find that only the equation y = -3/4x + 2 works for all the given points, which means it is the correct equation for the line representing the given points.