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What is the equation of the line perpendicular to line JY and whose y-intercept js -10

What Is The Equation Of The Line Perpendicular To Line JY And Whose Yintercept Js 10 class=

Sagot :

We will use the fact that two lines are perpendicular if the product of their slopes is -1, and that the slope-point form of the equation of a line is y=mx+b, where m is the slope and b is the y-intercept.

Now, the first step to solve this problem is to determine the slope of line JY, for that we will use the following formula:

[tex]s=\frac{y_1-y_2}{x_1-x_2},[/tex]

where y and x are the entries of two points on the line.

Using the above formula with the given points J and y we get, that the slope of the line JY is:

[tex]s=\frac{-4-5}{3-(-2)}=\frac{-9}{3+2}=\frac{-9}{5}=-\frac{9}{5}\text{.}[/tex]

Therefore, if S is the slope of the line perpendicular to JY then:

[tex]S\times-\frac{9}{5}=-1.[/tex]

Solving the above equation for S we get:

[tex]S=\frac{5}{9}\text{.}[/tex]

Finally, the slope-intercept form of the equation of the perpendicular line to JY is:

[tex]y=\frac{5}{9}x-10.[/tex]

Answer:

[tex]y=\frac{5}{9}x-10.[/tex]

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