Wrtite the slope intercept form of the equation of the line passing through point (5,1) and parallel to the line y=-4x-2.
The slope of the line will be -4.
The equation of the line is
(y-1) = -4(x-5)
which can be rewritten as
y = -4x +21
To write the slope-intercept form of the equation of a line, we need two key pieces of information: the slope of the line, and the y-intercept.
In this case, we are given that the line is parallel to the line y = -4x - 2. Two parallel lines have the same slope.
The given line y = -4x - 2 is in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. So, we can see that the slope of the given line is -4.
Since the parallel line we are looking for will have the same slope, we know that the slope of the line passing through (5, 1) is also -4.
Now that we have the slope, we can use the point-slope form of the equation of a line to find the equation of the line passing through (5, 1):
y - y₁ = m(x - x₁),
where (x₁, y₁) represents the given point (5, 1), and m is the slope we found (-4).
Substituting the values, we have:
y - 1 = -4(x - 5).
Now, we can simplify this equation:
y - 1 = -4x + 20.
To write it in the slope-intercept form, we isolate y:
y = -4x + 20 + 1,
y = -4x + 21.
Therefore, the slope-intercept form of the equation of the line passing through the point (5, 1) and parallel to the line y = -4x - 2 is y = -4x + 21.