Identify the slope of the line given by the equation y = -4x + 7.

Identify the slope of the line given by the equation y = -4x + 7.

• A. 2
• B. 0
• C. -2
• D. -4

Answer: (D)

Slope is the rate at which y changes as x changes, and in a line written as y = mx + b, the slope is the coefficient of x. Here, that coefficient is -4, so the slope is -4. This means for every 1 unit you move to the right, y decreases by 4. You can see this by checking with x replaced by x + 1: y becomes -4(x+1) + 7 = -4x + 7 - 4, which is the original y minus 4, confirming a drop of 4 per step to the right. Positive slopes would rise, zero would be flat, and -2 would be a gentler downward slope, so -4 is the correct slope.

Slope is the rate at which y changes as x changes, and in a line written as y = mx + b, the slope is the coefficient of x. Here, that coefficient is -4, so the slope is -4. This means for every 1 unit you move to the right, y decreases by 4. You can see this by checking with x replaced by x + 1: y becomes -4(x+1) + 7 = -4x + 7 - 4, which is the original y minus 4, confirming a drop of 4 per step to the right. Positive slopes would rise, zero would be flat, and -2 would be a gentler downward slope, so -4 is the correct slope.