Question

use the given conditions to write an equation for the line in point - slope form and in slope - intercept form. passing through (5, - 3) and perpendicular to the line whose equation is $y=\frac{1}{2}x + 3$... write an equation for the line in point - slope form. $y + 3=-2(x - 5)$ (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.)

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We already know from the point - slope form \(y + 3=-2(x - 5)\) that the slope \(m=-2\).

Step2: Expand the point - slope form

Start with the point - slope form \(y+3=-2(x - 5)\).
First, distribute the \(-2\) on the right - hand side: \(y + 3=-2x+10\).

Step3: Solve for y

Subtract 3 from both sides of the equation: \(y=-2x + 10-3\).
Simplify the right - hand side: \(y=-2x + 7\).

Answer:

\(y=-2x + 7\)