Find an equation of the line L, where L is perpendicular to y=3x and passes through the point (1,3)
Please help I'm not sure what formula to use or how to work out this problem
the slope of L is 3
so, the slope of all perpendiculars to L is -1/3
So, now you have a point and a slope.
If that doesn't tell you which form of the equation to use, there's trouble in River City.
I know how to get the slope. In my answer key it has the solution of -1\3x +10/3
What i don't get is how they got the +10/3 part
Y= -1/3 + 10/3
Why did the perpendicular line go to therapy? Because it had too many slope issues!
Don't worry, I can help you figure out the equation of the perpendicular line. First, let's find the slope of the given line y = 3x. In this equation, the coefficient of x is the slope, so the slope of the given line is 3.
To find the slope of the perpendicular line, we need to flip the slope and change the sign. The negative reciprocal of 3 is -1/3. So, the slope of the perpendicular line is -1/3.
Now we have the slope, we can use the point-slope form of a line to find the equation: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope of the line.
Plugging in the values, we get: y - 3 = (-1/3)(x - 1)
Now, let's solve this equation and simplify it to find the final equation of the perpendicular line. Happy solving!
To find the equation of a line that is perpendicular to another line, you need to determine the slope of the given line and then use the fact that perpendicular lines have slopes that are negative reciprocals of each other.
Let's start by finding the slope of the given line, y = 3x. The equation is already in slope-intercept form (y = mx + b) where m is the slope. In this case, the slope is 3. However, since we want a line perpendicular to this, we need to find the negative reciprocal of 3, which is -1/3.
Now that we have the slope of the line we are looking for, we can use the point-slope form of a linear equation: y - y₁ = m(x - x₁), where (x₁, y₁) is any point on the line and m is the slope.
Let's use the point (1,3) that the line passes through. Plugging in the values into the point-slope form, we get:
y - 3 = (-1/3)(x - 1)
Now we can simplify and rearrange the equation to slope-intercept form (y = mx + b):
y - 3 = (-1/3)x + 1/3
y = (-1/3)x + 10/3
Therefore, the equation of the line L that is perpendicular to y = 3x and passes through the point (1,3) is y = (-1/3)x + 10/3.