Question

What is the equation of a line that passes through the points (-3, 4) and (2,8)?

Answer 1

Given that the line passes through the two points (-3,4) and (2,8)

We need to determine the equation of the line.

Slope:

The slope of the line can be determined using the formula,

`m=(y_2-y_1)/(x_2-x_1)`

Substituting the points (-3,4) and (2,8) in the above formula, we get;

`m=(8-4)/(2+3)`

`m=(4)/(5)`

Thus, the slope of the line is
`m=(4)/(5)`

Equation of the line:

The equation of the line can be determined using the formula,

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

Substituting the point (-3,4) and
`m=(4)/(5)` in the above formula, we have;

`y-4=(4)/(5)(x+3)`

`y-4=(4)/(5)x+(12)/(5)`

`y=(4)/(5)x+(12)/(5)+4`

`y=(4)/(5)x+(32)/(5)`

Thus, the equation of the line is
`y=(4)/(5)x+(32)/(5)`