Question

A line passes through `(5 ,0 )` and `(7 ,9 )`. A second line passes through `(3 ,6 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

`(2,3/2)`

Explanation:

`"establish the equation of the parallel line"`

`"the equation of a line in "color(blue)"slope-intercept form "` is.

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`"to calculate m use the "color(blue)"gradient formula"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))`

`"let "(x_1,y_1)=(5,0)" and "(x_2,y_2)=(7,9)`

`rArrm=(9-0)/(7-5)=9/2`

`• " parallel lines have equal slopes"`

`rArr"slope of parallel line "=9/2`

`rArry=9/2x+b color(blue)" is the partial equation"`

`"to find b substitute "(3,6)" into the partial equation"`

`6=27/2+brArrb=-15/2`

`rArry=9/2x-15/2larrcolor(blue)"equation of parallel line"`

`"choose any value for x and substitute into the equation"`

`x=2toy=9-15/2=3/2`

`"another point on the line is "(2,3/2)`