Question

What is the equation of the line described below written in slope-iWhat is the equation of the line described below written in slope-intercept form?

the line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0

Answer 1

The equation of a line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0 is y = -1/2x + 1

Equation of a line

A line is the shortest distance between two points. The equation of a line in point-slope form and perpendicular to a line is given as;

y - y1 = -1/m(x-x1)

where

m is the slope

(x1, y1) is the intercept

Given the following

Point = (4, -1)

Line: 2x-y - 7 = 0

Determine the slope

-y = -2x + 7

y= 2x - 7

Slope = 2

Substitute

y+1 = -1/2(x -4)

Write in slope-intercept form

2(y + 1) = -(x - 4)

2y+2 = -x + 4

2y = -x + 2

y = -1/2 + 1

Hence the equation of a line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0 is y = -1/2x + 1

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