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Line and point V are shown on the graph.


Line is to be drawn on the graph such that it is perpendicular to line . If the coordinates of point W are (–1, y), what is the value of y?

Line and point V are shown on the graph Line is to be drawn on the graph such that it is perpendicular to line If the coordinates of point W are 1 y what is the class=

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sqdancefan
If you want line VW to be perpendicular to line ST, which has slope 1/5, you want to find y such that
  (y-(-2))/(0-(-1)) = -1/(1/5) . . . . the perpendicular line has a slope that is the negative reciprocal of the slope of line ST.
  y + 2 = 5
  y = 3
calculista

Answer:

The y-coordinate of point W is [tex]3[/tex]

Step-by-step explanation:

Step 1

Fin the slope of the line ST

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

[tex]S(-5,0)\ T(5,2)[/tex]

Substitute the values

[tex]m=\frac{2-0}{5+5}[/tex]

[tex]m=\frac{2}{10}[/tex]

[tex]m=\frac{1}{5}[/tex]

Step 2

Find the slope of the line WV

we know that

If two lines are perpendicular, then the product of their slopes is equal to minus one

so

[tex]m1*m2=-1[/tex]-------> [tex]mST*mWV=-1[/tex]

we have

[tex]mST=\frac{1}{5}[/tex]

substitute the value and solve for mWV

[tex]\frac{1}{5}*mWV=-1[/tex]

[tex]mWV=-5[/tex]

Step 3

Find the equation of the line WV into slope-intercept form

[tex]y=mx+b[/tex]

we have

[tex]m=-5[/tex]

[tex]b=-2[/tex]  -------> see the graph Point V is the y-intercept of the line WV

substitute

[tex]y=-5x-2[/tex]

Step 4

Find the y-coordinate of the point W

[tex]W(-1,y)[/tex]

Substitute the the values of x and y of point W in the linear equation

[tex]y=-5(-1)-2[/tex]

[tex]y=3[/tex]

therefore

the y-coordinate of point W is [tex]3[/tex]


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