Question

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?

Answer 1

The y-coordinate of point W is
`3`

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

`m=(y2-y1)/(x2-x1)`

we have

`S(-5,0)\ T(5,2)`

Substitute the values

`m=(2-0)/(5+5)`

`m=(2)/(10)`

`m=(1)/(5)`

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

`m1*m2=-1`------->
`mST*mWV=-1`

we have

`mST=(1)/(5)`

substitute the value and solve for mWV

`(1)/(5)*mWV=-1`

`mWV=-5`

Step 3

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

`y=mx+b`

we have

`m=-5`

`b=-2` -------> see the graph Point V is the y-intercept of the line WV

substitute

`y=-5x-2`

Step 4

Find the y-coordinate of the point W

`W(-1,y)`

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

`y=-5(-1)-2`

`y=3`

therefore

the y-coordinate of point W is
`3`

Answer 2

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