write the equation of the line perpendicular to y=5x-3 passing through the point (10,2)
you want a line with slope -1/5
so, using the point-slope form,
y-2 = -1/5 (x-10)
To find the equation of a line perpendicular to a given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
The given equation is y = 5x - 3.
The slope of this line can be determined by comparing the equation with the standard form y = mx + b, where m represents the slope. In this case, the slope is 5.
To find the negative reciprocal of the slope, we take its reciprocal (1/5) and multiply by -1, resulting in -1/5.
We now have the slope (-1/5) and the point (10, 2).
Using the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) represents a point and m is the slope, we can substitute the values into the equation:
y - 2 = (-1/5)(x - 10)
Simplifying further, we distribute the -1/5 to the terms inside the parentheses:
y - 2 = (-1/5)x + 2
Adding 2 to both sides to isolate y, we get:
y = (-1/5)x + 4
Therefore, the equation of the line perpendicular to y = 5x - 3 and passing through the point (10, 2) is y = (-1/5)x + 4.
To find the equation of the line that is perpendicular to the given line, we first need to determine the slope of the given line. In the equation y = 5x - 3, we can see that the coefficient of x is 5, which represents the slope of the line.
The slope of the perpendicular line can be found by taking the negative reciprocal of the slope of the given line. The negative reciprocal of 5 is -1/5.
Now that we have the slope (-1/5) and a point (10, 2), we can utilize the point-slope form of a linear equation to find the equation of the perpendicular line.
The point-slope form is given by:
y - y₁ = m(x - x₁)
Where (x₁, y₁) is the given point and m is the slope.
Substituting the values into the equation, we have:
y - 2 = (-1/5)(x - 10)
Next, we can simplify the equation by distributing -1/5 into (x - 10):
y - 2 = (-1/5)x + 2
To isolate y, we can add 2 to both sides of the equation:
y = (-1/5)x + 2 + 2
y = (-1/5)x + 4
Therefore, the equation of the line perpendicular to y = 5x - 3 and passing through the point (10, 2) is y = (-1/5)x + 4.