Final answer:
The equation of the line passing through the given points (-4, -2) and (14, 4) in slope-intercept form is y = (1/3)x - (2/3).
Step-by-step explanation:
To write the equation of a line in slope-intercept form, we need to find the slope between the two given points and the y-intercept.
First, let's find the slope:
Slope ($m$) = $rac{{ ext{{change in }} y}}{{ ext{{change in }} x}}$
Using the formula, we have:
Slope ($m$) = $rac{{ ext{{change in }} y}}{{ ext{{change in }} x}} = rac{{4 - (-2)}}{{14 - (-4)}} = rac{{6}}{{18}} = rac{1}{3}$
Next, let's find the y-intercept ($b$). We can use one of the given points.
Using the point (-4, -2):
$y = mx + b$
$-2 = rac{1}{3}(-4) + b$
$-2 = -rac{4}{3} + b$
$-2 + rac{4}{3} = b$
$-rac{6}{3} + rac{4}{3} = b$
$-rac{2}{3} = b$
Now we can write the equation of the line in slope-intercept form:
$y = mx + b$
$y = rac{1}{3}x - rac{2}{3}$
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