Question

A line passes through `(3 ,6 )` and `(4 ,8 )`. A second line passes through `(7 ,9 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

`(1,-3)`

Explanation:

`"one way is to establish the equation of the line passing"`
`"through "(7,9)" and find points that lie on it"`

`• " parallel lines have equal slopes"`

`"find the slope (m) using 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)=(3,6)" and "(x_2,y_2)=(4,8)`

`rArrm=(8-6)/(4-3)=2`

`"the equation of the line through "(7,9)`

`y=2x+blarrcolor(blue)"slope-intercept form"`

`"to find b substitute "(7,9)" into the equation"`

`9=14+brArrb=-5`

`rArry=2x-5larrcolor(blue)"equation of line"`

`"choosing any value for x and evaluate for y"`

`x=1toy=2-5=-3`

`rArr(1,-3)" is a point on the second line"`