Question

What is the equation of the line that passes through the points (-1, 1.5) and (0.5, 0.5)

Answer 1

The slope-point formula:

`y-y_1=m(x-x_1)\\\\m=(y_2-y_1)/(x_2-x_1)`

We have:

`(-1,\ 1.5)\to x_1=-1,\ y_1=1.5\\(0.5,\ 0.5)\to x_2=0.5,\ y_2=0.5`

Substitute:

`m=(0.5-1.5)/(0.5-(-1))=(-1)/(1.5)=-(1)/((3)/(2))=-(2)/(3)\\\\y-1.5=-(2)/(3)(x-(-1))\\\\y-1.5=-(2)/(3)x-(2)/(3)\\\\y-(3)/(2)=-(2)/(3)x-(2)/(3)\ \ \ |+(3)/(2)\\\\y=-(2)/(3)x-(2)/(3)+(3)/(2)\\\\y=-(2)/(3)x-(2\cdot2)/(3\cdot2)+(3\cdot3)/(2\cdot3)\\\\y=-(2)/(3)x-(4)/(6)+(9)/(6)\\\\y=-(2)/(3)x+(5)/(6)`