Write an equation for line k that is perpendicular to line j and passes through points (1,1)
What is the equation for line j?
To find the equation of a line that is perpendicular to line j and passes through the point (1,1), we need to determine the slope of line j first.
If you know the equation of line j, you can find its slope by using the formula: slope = (change in y)/(change in x).
With the slope of line j in hand, you can find the slope of the line perpendicular to line j by using the relationship that the product of the slopes of perpendicular lines is -1. This means that the slope of the desired line, let's call it line k, will be the negative reciprocal of the slope of line j.
Once you have the slope of line k, you can use the point-slope form of a linear equation to find the equation of line k. The point-slope form is:
y - y₁ = m(x - x₁),
where (x₁, y₁) is the given point through which the line passes, and m is the slope of the line.
Here's a step-by-step approach to finding the equation:
1. Determine the slope of line j using the given equation or two points on the line.
2. Find the negative reciprocal of the slope of line j to get the slope of line k.
3. Plug the values of the slope and the point (1, 1) into the point-slope form equation.
4. Simplify the equation to get it into the desired form (slope-intercept form, standard form, etc.) if needed.
If you can provide the equation of line j or two points on line j, I can help you calculate the slope and provide the equation for line k.