Write the equation of the line that is perpendicular to 10x=-y and passes through point (4,2/5)
To find the equation of a line perpendicular to the given line, we need to find the slope of the given line first.
Rewriting the given equation in slope-intercept form (y = mx + b), we have:
10x = -y
Rewriting as -y = 10x, we have:
y = -10x
Comparing this with the slope-intercept form, we see that the slope (m) is -10.
Since the line we want is perpendicular to this line, its slope will be the negative reciprocal of -10, which is 1/10.
Now, we have the slope (m) and a point (4, 2/5). We can use the point-slope form of a line to find the equation.
The point-slope form is given by:
y - y₁ = m(x - x₁)
Plugging in the values, the equation becomes:
y - (2/5) = (1/10)(x - 4)
Multiplying through by 10 to eliminate fractions, we have:
10y - 4 = x - 4
Rearranging the terms, we get:
x - 10y = 0
So, the equation of the line that is perpendicular to 10x = -y and passes through the point (4, 2/5) is x - 10y = 0.
To find the equation of a line that is perpendicular to a given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
Let's start by rewriting the given equation in slope-intercept form (y = mx + b), where m represents the slope:
10x = -y
Dividing both sides of the equation by -1, we get:
-10x = y
Now, in slope-intercept form, the equation becomes:
y = -10x
We can see that the slope of the given line is -10.
The negative reciprocal of -10 is 1/10. So, the slope of the perpendicular line will be 1/10.
Now, let's use the point-slope form of a line to find the equation. The formula is given as:
y - y1 = m(x - x1),
where (x1, y1) represents the coordinates of the given point and m is the slope.
Substituting the values into the equation:
y - 2/5 = (1/10)(x - 4)
Simplifying:
y - 2/5 = (1/10)x - 4/10
y - 2/5 = (1/10)x - 2/5
Adding 2/5 to both sides:
y = (1/10)x - 2/5 + 2/5
y = (1/10)x
Therefore, the equation of the line that is perpendicular to 10x = -y and passes through the point (4, 2/5) is y = (1/10)x.