Question

Which is the equation of the line that passes through the point (-4,3) and (2,6)

Answer 1

`\displaystyle y = (1)/(2)x + 5`

Explanation:

Equation of a Line

The point-slope form of the equation of a line is:

y - k = m ( x - h )

Where m is the slope and (h,k) is a point through which the line passes.

Suppose a line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the formula:

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

We'll use the points (-4,3) and (2,6), thus:

`\displaystyle m=(6-3)/(2+4)=(3)/(6)=(1)/(2)`

Now we use the point-slope form using the point (2,6):

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

Operating:

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

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

`\boxed{\displaystyle y = (1)/(2)x + 5}`