Question

question
what is an equation of the line that passes through the point (6, -4) and is parallel to the line x + y = 9?
answer attempt 1 out of 2
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Explanation:

Step1: Find the slope of the given line

The given line is \(x + y=9\). Rewrite it in slope - intercept form \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept).
Subtract \(x\) from both sides: \(y=-x + 9\). So the slope \(m\) of the line \(x + y = 9\) is \(- 1\).

Step2: Use the point - slope form for the parallel line

Since parallel lines have the same slope, the line we want to find also has a slope \(m=-1\).
The point - slope form of a line is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)=(6,-4)\) and \(m = - 1\).
Substitute the values into the point - slope form: \(y-(-4)=-1(x - 6)\).

Step3: Simplify the equation

Simplify \(y + 4=-x + 6\).
Subtract 4 from both sides: \(y=-x+6 - 4\), which gives \(y=-x + 2\).
We can also rewrite it in the general form \(x + y=2\).

Answer:

The equation of the line is \(x + y = 2\) (or \(y=-x + 2\))