Consider the linear function that is represented by the equation y=-10x+6 and the linear function that is represented by the equation y-36=8(x-4). Which statement is correct regarding their slopes and y-intercepts?

a. The function that is represented by the equation y=-10x+6 has a steeper slope and a greater y-intercept.

b. The function that is represented by the equation y=-10x+6 has a steeper slope, and the function that is represented by the equation y-36=8(x-4) has a greater y-intercept.

c. The function that is represented by the equation y-36=8(x-4) has a steeper slope, and the function that is represented by the equation y=-10x+6 has a greater y-intercept.

d. The function that is represented by the equation y-36=8(x-4) has a steeper slope and a greater y-intercept.

Respuesta :

The function that is represented by the equation y=-10x+6 has a steeper slope and a greater y-intercept.

This is about understanding slopes.

Option A is correct.

  • We are given two linear functions which are;

y = -10x + 6  - - - (eq 1)

y - 36 = 8(x - 4)  - - - (eq 2)

  • Formula for straight line equation is;

y = mx + c

Where m is slope and c is the y intercept.

Let's expand eq 2 to be in the form of y = mx + c

Thus;

>>y - 36 = 8(x - 4)

>> y - 36 = 8x - 32

>> y = 8x - 32 + 36

>> y = 8x + 4  - - - (eq 3)

Thus, slope of eq 1 is -10 and y-intercept is 6.

Similarly, slope of eq 3 is 8 and y-intercept is 4.

This means y = -10x + 6 has a greater y-intercept than y - 36 = 8(x - 4).

Also, the slope in y - 36 = 8(x - 4) which is 8 will slope to the right while the slope of y = -10x + 6  which is -10 will slope to the left. This means that line represented by y = -10x + 6  has a steeper slope.

This is because the higher the slope, the steeper the line.

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