Question

The line L passes through the points (0, –2) and (6, 1).

Find an equation of the line L.

Answer 1

The equation for line L is, y=-1/6x+2

Answer 2

an equation of the line L will be: y = 1/2x - 2

Explanation:

The slope-intercept form of the line equation

y = mx+b

where

• m is the slope

• b is the y-intercept

Given the points

• (0, -2)

• (6, 1)

Determining the slope between (0, -2) and (6, 1)

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(0,\:-2\right),\:\left(x_2,\:y_2\right)=\left(6,\:1\right)`

`m=(1-\left(-2\right))/(6-0)`

`m=(1)/(2)`

The y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

From the point (0, -2), we can determine that at x = 0, the value of y = -2.

Thus,

The y-intercept b = -2

now substituting b = -2 and m = 1/2 in the slope-intercept form of line equation

y = mx+b

y = 1/2x + -2

y = 1/2x - 2

Therefore, an equation of the line L will be: y = 1/2x - 2