what is the equation of the line given the following conditions.
6. Passing through (-8, -10) and parallel to the line whose equation is y = -4x + 3
Since it is parallel, it must differ only in the constant, so let
y = -4x + b
sub in the given point, find b, and you are done
P(-8, -10), m = -4.
Y = mx + b.
-10 = -4*(-8) + b,
Y = -4x - 42.
To find the equation of a line parallel to another line, we need to remember that parallel lines have the same slope.
The given equation of the line is y = -4x + 3. We can see that the slope of this line is -4, as the coefficient of x is -4.
Since the line we want to find is parallel, it will have the same slope of -4.
Now, we have the slope (-4) and a point on the line (-8, -10). We can use the point-slope formula to find the equation of the line, which is:
y - y1 = m(x - x1)
where m represents the slope and (x1, y1) represents the coordinates of the given point.
Substituting the given values, we have:
y - (-10) = (-4)(x - (-8))
Simplifying further:
y + 10 = -4(x + 8)
Now, let's distribute the -4 on the right hand side:
y + 10 = -4x - 32
To isolate y, we subtract 10 from both sides:
y = -4x - 42
Therefore, the equation of the line passing through (-8, -10) and parallel to y = -4x + 3 is y = -4x - 42.