Mathematics: The line L passes through the points (0, –2) and (6, 1). Find an equation of the line L.

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

emmacox069

17.03.2022

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

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

m is the slopeb is the y-intercept

Given the points

(0, -2)(6, 1)

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

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

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

$m=\frac{1-\left(-2\right)}{6-0}$

$m=\frac{1}{2}$

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

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