OG详解-OG10 数学2 Q21

The correct answer is 1​4​. For an equation in slope-intercept form y = mx+b, m represents the slope of the line in the xy-plane defined by this equation. It’s given that line l is defined by 3y+12x = 5. Subtracting 12x from both sides of this equation yields 3y = -12x+5. Dividing both sides of this equation by 3 yields y =−123​x+5​3​, or y = -4x+5​3​. Thus, the slope of line l in the xy-plane is -4. Since line n is perpendicular to line l in the xy-plane, the slope of line n is the negative reciprocal of the slope of line l. The negative reciprocal of -4 is - 1(−4)​=1​4​. Note that 1/4 and .25 are examples of ways to enter a correct answer.