Write an equation in slope-intercept form perpendicular

Ответ:

lacourboud20005

17.03.2022

The equation in slope-intercept form perpendicular to the given equation y = -3x + 4 through the given point (6,-2) is $\mathbf{y=\frac{1}{3}x}$

Step-by-step explanation:

We need to write an equation in slope-intercept form perpendicular to the given equation through the given point

y = -3x + 4

(6,-2)

The general equation in slope intercept form is: y=mx+b where m is slope and b is y-intercept.

We need to find slope and y-intercept.

Finding slope:

The given line is perpendicular to required line, so there slopes are opposite

The slope of given line y = -3x + 4 is m = -3, (By comparing it with general equation y=mx+b, we get m = -3)

The slope of required line is: $m = \frac{1}{3}$

Finding y-intercept:

y-intercept can be found by using slope $m = \frac{1}{3}$ and the point(6,-2)

$y=mx+b\\-2=\frac{1}{3}(-6)+b\\-2=-2+b\\b=-2+2\\b=0$

So, we get y-intercept b =0

Equation of required line:

So, the equation of required line having slope $m = \frac{1}{3}$ and y-intercept b =0 is:

$y=mx+b\\y=\frac{1}{3}x+0\\y=\frac{1}{3}x$

So, the equation in slope-intercept form perpendicular to the given equation y = -3x + 4 through the given point (6,-2) is $\mathbf{y=\frac{1}{3}x}$

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