Final answer:
To find the line parallel to y = 2/3x + 1 that passes through (-5, -2), first recognize that parallel lines share the same slope, which is 2/3. Then use the point-slope equation with the given point, resulting in the equation y =( 2/3)x + (4/3).
Step-by-step explanation:
To find the line that passes through the point (-5, -2) and is parallel to the equation y = \(\frac{2}{3}x\) + 1, we first recognize that parallel lines have the same slope. The slope (m) of the given line is \(\frac{2}{3}, so the slope of the line we are trying to find will be the same. We then use the point-slope form of the equation of a line, y - y_1 = m(x - x_1), where (x_1, y_1) is the point the line passes through, and m is the slope of the line.
Plugging the point (-5, -2) and the slope \(\frac{2}{3} into the point-slope form, the equation of the line parallel to y = \(\frac{2}{3}x\) + 1 and passing through the point (-5, -2) is:
y + 2 = \(\frac{2}{3}(x + 5)\)
y = \(\frac{2}{3}x\) + \(\frac{10}{3}\) - 2
y = \(\frac{2}{3}x\) + \(\frac{4}{3}\)
Therefore, the line that we are looking for is y = \(\frac{2}{3}x\) + \(\frac{4}{3}\).