Question

question 2 of 5. select the correct answer. a graphic designer is creating a logo for a client. lines db and ac are perpendicular. the equation of db is 1/2x + 2y = 12. what is the equation of ac? -4x + y = -28, 2x + y = 14, 4x - y = -28, 2x + 8y = 12

Explanation:

Step1: Rewrite the equation of line DB in slope - intercept form

Given $\frac{1}{2}x + 2y=12$, solve for $y$. First, subtract $\frac{1}{2}x$ from both sides: $2y=-\frac{1}{2}x + 12$. Then divide by 2: $y =-\frac{1}{4}x+6$. The slope of line DB, $m_{DB}=-\frac{1}{4}$.

Step2: Use the slope - relationship for perpendicular lines

If two lines are perpendicular, the product of their slopes is - 1. Let the slope of line AC be $m_{AC}$. Since $m_{DB}\times m_{AC}=-1$, and $m_{DB}=-\frac{1}{4}$, then $-\frac{1}{4}m_{AC}=-1$. Solving for $m_{AC}$ gives $m_{AC} = 4$.

Step3: Use the point - slope form to find the equation of line AC

We can use the point - slope form $y - y_1=m(x - x_1)$. Let's assume we use the mid - point of AC (the intersection of AC and DB) which we can find from the system of equations of the two lines. Another way is to use the fact that we can check the equations with the slope. Let's rewrite the given equations in slope - intercept form $y=mx + b$.
For the equation $4x-y=-28$, rewrite it as $y = 4x + 28$. The slope of this line is 4 which is the slope we found for line AC.

Answer:

$4x - y=-28$