Question

What is the slope of a line perpendicular to the line whose equation is 4x+5y=35. Fully simplify your answer.

Answer 1

Answer:

The slope a line perpendicular to the line whose equation is 4x+5y=35, is $\frac{5}{4}$.

Step-by-step explanation:

1. Solve the given equation for y.

$4x+5y=35\\\\5y=35-4x\\\\\frac{5y}{5} =\frac{35}{5} -\frac{4x}{5} \\\\y =7 -\frac{4x}{5}\\\\y = -\frac{4}{5}x+7$

2. Identify the slope.

The slope of a linear equation is always the number x is being multiplied for. Hence, the value of this equation is $-\frac{4}{5}$ .

3. Find the slope of the perpendicular line.

The slope of a perpendicular line is always the multiplicative and addition reciprocal of the initial function. This means that you will have to invert and fracction, and add the inverse sign before it. Let's do it by parts:

a) Find the multiplicative reciprocal (invert the fraction).

$-\frac{5}{4}$

b) Put the opposite sign before the fraction.

$+\frac{5}{4}$

4. Express a result.

The slope a line perpendicular to the line whose equation is 4x+5y=35, is $\frac{5}{4}$.