gh The Point (3,4). What Is The Equation Of Line N?
To find the equation of Line N, we need to first understand what it means for two lines to be parallel. In geometry, parallel lines are lines in the same plane that do not intersect and they have the same slope.
Given that Line N is parallel to Line K, Line N must also have the same slope as Line K.
From the equation of Line K, which is y = -x + 17, we can see that the slope of the line, represented by the coefficient of x, is -1. Hence, the slope of Line N is also -1.
Now we know the slope of Line N, we can use the Point-Slope form of an equation of a line to find its equation. The Point-Slope form is shown as y - y1 = m(x - x1), where m is the slope, and (x1, y1) is a point that lies on the line.
In this case, we are given that Line N passes through the point (3, 4), so x1 is 3, and y1 is 4.
If we plug these values into the Point-Slope formula, we have y - 4 = -1(x - 3).
Solving the equation leads to y - 4 = -x + 3.
If we simplify this, by adding 'x' and '4' to both sides, it will give us the equation of Line N: y = -x + 7.
So, the equation of line N which is parallel to line K and passes through (3, 4) is y = -x + 7.