equation of the line
find the equation of the line that passes through the
intersection of the given fair of lines and satisfies
the oher given condition.
3x+5y-2=0, x+y +2= 0; passes through (-4,-2)
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1) 3x + 5y - 2 = 0
2) x + y + 2 = 0
From equation 2: x = -y - 2
Substitute into equation 1.
3x + 5y - 2 = 0
3(-y -2) + 5y - 2 = 0
-3y - 6 + 5y - 2 = 0
2y - 8 = 0
2y = 8
y = 4
Use equation 2 again.
x + y + 2 = 0
x + 4 + 2 = 0
x + 6 = 0
x = -6
The intersection is (-6, 4)
Determine the equation of the line that passes
through the intersection, (-6, 4), and the point
specified in the problem statement, (-4, -2).
m = (y2 - y1) / (x2 - x1)
m = (-2 - 4) / (-4 - (-6))
m = -6 / (-4 + 6)
m = -6 / 2
m = -3
Calculate the y-intercept, using the given point, (-4, -2).
y = mx + b
y - mx = b
b = y - mx
b = -2 - (-3)(-4)
b = -2 - 12
b = -14
The requested equation is y = -3x - 14.