Write an equation in slope-intercept form for the line parallel to y = 5x - 2 that passes through the point (8, -2)
or
a line parallel to y = 5x - 2 is
y = 5x + b , but (8,-2) lies on it
-2 = 40 + b
b = -42
y = 5x - 42
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5x-2 passes through (8,38)
So, you need to subtract 40 so it goes through (8,-2)
To find the equation of a line parallel to y = 5x - 2, we need to know that parallel lines have the same slope. So, the slope of the new line will be 5.
Using the point-slope form of the equation of a line, we can calculate the equation of the line using the given point (8, -2) and the slope of 5.
The point-slope form of the equation is: y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.
Substituting the given point (8, -2) and the slope of 5 into the equation, we have:
y - (-2) = 5(x - 8)
Simplifying:
y + 2 = 5x - 40
Now, to write the equation in slope-intercept form (y = mx + b), we need to isolate y on one side:
y = 5x - 40 - 2
y = 5x - 42
Therefore, the equation of the line parallel to y = 5x - 2 that passes through the point (8, -2) is y = 5x - 42.