Question

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

Answer 1

Answer:

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

                         $y=x+11$

Step-by-step explanation:

The line GH passes through:

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

The slope of a given line GH is given by:

$Slope(m)=\dfrac{6-2}{2-(-2)}\\\\\\Slope(m)=\dfrac{4}{4}\\\\\\i.e.\\\\\\Slope(m)=1$

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:

                     $y=x+11$

Answer 2

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.