Question

Which equation best represents the line a y=3/4×+4 b y=4/3x+4 c y=4x+3/4 d =4x+4/3

Answer 1

The line is best represented by equation a. y =
`(3)/(4)`x + 4

Explanation:

Step 1; The first step is to identify as many coordinates of the points which are on the line. We check to see if the line passes through any points which occur on any whole number on the x and y axes i.e. axis lengths such as 1,2,3 and so on. By observation of the graph, we find that three such points satisfy these conditions. The three points being (0,4), (-4,1) and (4,7).

Step 2; We substitute the coordinates in the four given equations to see which equation satisfies it. First, we will take the point (4,7) and substitute in the place of x 4 and in the place of y 7.

Equation 1; y =
`(3)/(4)`x + 4, 7 =
`(3)/(4)`×4 + 4 = 3 + 4 = 7, 7 = 7.

Equation 2; y =
`(4)/(3)`x + 4, 7 =
`(4)/(3)`×4 + 4 = 9.33, 7 ≠ 9.33.

Equation 3; y = 4x +
`(3)/(4)`, 7 = 4×4 +
`(3)/(4)` = 16.75, 7 ≠ 16.75.

Equation 4; y = 4x +
`(4)/(3)`, 7 = 4×4 +
`(4)/(3)` = 17.33, 7 ≠ 17.33.

So equation 1 alone satisfies the equation.

Step 3; The other points (0,4), (-4,1) are also substituted in the equation and are found to satisfy the equations. So equation 1 y =
`(3)/(4)`x + 4 represents the line.