Question

What is the a line that passes through (-2,5) and has a slope of 2/3. Points A(x,3) and B(-2,y) lie on the line

Answer 1

The point-slope form of linear equation is:


`y-y_1=m(x-x_1)`

Hence,


`\displaystyle y-5= (2)/(3)(x+2)\\\\y= (2)/(3)x+5 (4)/(3) \\\\y=(2)/(3)x+6 (1)/(3)`

The points A,B are lying on the line, if and only if the next equality is true:

`\displaystyle y=(2)/(3)x+6 (1)/(3)`

Therefore,

`\displaystyle A(x,3) \Rightarrow\\\\3=(2)/(3)x+6 (1)/(3) \\\\9=2x+19\\\\-10=2x\\\\x=-5`


`\displaystyle B(-2,y)\Rightarrow \\\\y=(-4)/(3)+6 (1)/(3) \\\\y=5`