Question

Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.1Passing through (6. - 5) and perpendicular to the line whose equation is y= 2x+5Write an equation for the line in point-slope form.(Simplify your answer. Use integers or fractions for any numbers in the equation)Write an equation for the line in slope-intercept form.(Simplify your answer. Use integers or fractions for any numbers in the equation)anand

Answer 1

Given:

The line is perpendicular to the line whose equation is

$y\text{ = }\frac{1}{4}x\text{ + 5}$

It passes through the point (6, -5)

A line with a slope (m) is perpendicular with another line with a slope (m*) if:

$m\text{ }\times m^{\cdot}\text{ = -1}$

The slope of the line would thus be:

$\begin{gathered} \text{slope = }\frac{-1}{\frac{1}{4}} \\ =\text{ -4} \end{gathered}$

In point-slope form:

$\begin{gathered} y\text{ - (-5) = -4(x-6)} \\ y\text{ + 5 = -4(x -6)} \end{gathered}$

In slope-intercept form:

$\begin{gathered} y+\text{ 5 = -4(x-6)} \\ y\text{ + 5 = -4x + 24} \\ y\text{ = -4x + 24 - 5} \\ y\text{ = -4x + 19} \end{gathered}$