Question

Write an equation of a line in slope-intercept form that is perpendicular to the line to y = -2x - 1 and that passes through the point (-10,4)

Answer 1

Answer:$y\text{ = }\frac{1}{2}x\text{ + 9}$Explanations:

The slope - Intercept form of the equation of a line is written as:

y = mx + c...........................(1)

where m is the slope and

c is the intercept

the equation given in this task is:

y = -2x - 1..........................(2)

Comparing equations (1) and (2)

m = -2

That is the slope of the line = -2

A line perpendicular to the line y = -2x - 1 will have a slope:

$\begin{gathered} m_1=\text{ }\frac{-1}{m} \\ m_1=\text{ }\frac{-1}{-2} \\ m_1=\text{ }\frac{1}{2} \end{gathered}$

The equation of the perpendicular line will be:

$y-y_1=m_1(x-x_1)$

The point through which the line passes is (-10, 4)

That is, x₁ = -10, y₁ = 4

The equation of the perpendicular line becomes:

$\begin{gathered} y\text{ - 4 = }\frac{1}{2}(x\text{ - (-10))} \\ y\text{ - 4 = }\frac{1}{2}(x\text{ + 10)} \\ y-\text{ 4 = }\frac{x}{2}+\text{ }\frac{10}{2} \\ y\text{ - 4 = }\frac{x}{2}\text{ + 5} \\ y\text{ = }\frac{x}{2}\text{ + 5 + 4} \\ y\text{ = }\frac{x}{2}\text{ + 9} \\ y\text{ = }\frac{1}{2}x\text{ + 9} \end{gathered}$