Question

Write an equation of a line parallel to line GH below in slope-intercept form that passes through the point (−5, 6).

y = −x − 1
y = x − 1
y = −x + 11
y = x + 11

Hello! I think it is the last one but I'm not sure!! I appreciate any help! Thank you : ) !!

Answer 1

The slope of GH is 1, so any line parallel to GH will have the same slope.

Since this other line passes through (-5,6), you can use the point-slope formula:


`y-6=1(x-(-5))\implies y-6=x+5\implies y=x+11`

so you are correct.

Answer 2

The equation of a line parallel to line GH in slope-intercept form that passes through the point (−5, 6) is:

`y=x+11`

Explanation:

The line GH passes through:

(-2,2) and (2,6)

The slope of a given line GH is given by:

`Slope(m)=(6-2)/(2-(-2))\\\\\\Slope(m)=(4)/(4)\\\\\\i.e.\\\\\\Slope(m)=1`

We know that if a line is parallel to a given line than both have the same slope.

i.e. the slope of second line is: 1

Also, we know that a equation of a line with given slope "m" and passing through point (a,b) is given by:

`y-b=m(x-a)`

Here we have m=1

and (a,b)=(-5,6)

and hence the equation of parallel line is:

`y-6=1(x-(-5))\\\\\\i.e.\\\\\\y-6=x+5\\\\\\i.e.\\\\\\y=x+5+6\\\\\\i.e.\\\\\\y=x+11`

Hence, the equation is:

`y=x+11`