Question

The graph shows a line through the points -2,-2 and 2,0 . consider the line parallel to this line through the point 4,4 . where will the parallel line cross the y-axis (it's y-intercept) ?

Answer 1

The parallel line cross the y-axis at point (0,6)

Explanation:

we know that

If two lines are parallel, then their slopes are equal

step 1

Find the slope of the line that pass through the points (-2,2) and (2,0)

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

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

substitute the values

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

`m=(-2)/(4)`

`m=-(1)/(2)`

step 2

Find the equation of the line parallel to the given line and pass through the point (4,4)

The equation of a line in point slope form is

`y-y1=m(x-x1)`

we have

`m=-(1)/(2)` --> remember that in parallel lines the slopes are the same

`point\ (4,4)`

substitute

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

Convert to slope intercept form

isolate the variable y

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

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

`y=-(1)/(2)x+6`

step 3

Find the y-intercept

Remember that the y-intercept is the value of y when the value of x is equal to zero

so

For x=0

`y=-(1)/(2)(0)+6`

`y=6`

therefore

The parallel line cross the y-axis at point (0,6)