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Answer (assuming it can be put in point-slope format):
[tex]y + 4 = 3(x-2)[/tex]
Step-by-step explanation:
You can write an equation of a line when knowing its slope and a line it passes through using point slope formula, [tex]y-y_1 = m (x-x_1)[/tex].
1) First, find the slope of the equation. We know it has to be parallel to y = 3x + 2. Lines that are parallel have the same slope, thus the slope of y = 3x + 2 is the slope of the answer as well. y = 3x + 2 is in slope-intercept format, or [tex]y = mx + b[/tex]. The coefficient of the x term, or [tex]m[/tex], represents the slope - so, the slope must be 3.
2) Now, use point-slope formula,[tex]y-y_1 = m (x-x_1)[/tex], to write the equation. Substitute [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] for real values.
The [tex]m[/tex] represents the slope, so substitute 3 for [tex]m[/tex]. The [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line crosses through. The line crosses through (2, -4), so substitute 2 for [tex]x_1[/tex] and -4 for [tex]y_1[/tex]. This gives the following answer:
[tex]y - (-4) = 3 (x-(2))\\y + 4 = 3(x-2)[/tex]