Question

what is the equation of the line that passes through the point (-4, 8) and has a slope of -1? answer attempt 1 out of 2

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation is given by \(y - y_1=m(x - x_1)\), where \((x_1,y_1)\) is a point on the line and \(m\) is the slope of the line.
Here, \(x_1=-4\), \(y_1 = 8\) and \(m=-1\).

Step2: Substitute values into point - slope form

Substitute \(x_1=-4\), \(y_1 = 8\) and \(m = - 1\) into the point - slope formula:
\(y-8=-1(x - (-4))\)
Simplify the right - hand side: \(y - 8=-1(x + 4)\)

Step3: Convert to slope - intercept form (optional, but to get a more standard form)

Expand the right - hand side: \(y-8=-x - 4\)
Add 8 to both sides of the equation: \(y=-x - 4 + 8\)
Simplify the constant terms: \(y=-x+4\)
We can also write it in the standard form \(x + y=4\), but the slope - intercept form \(y=-x + 4\) is also correct.

Answer:

\(y=-x + 4\) (or \(x + y=4\) or other equivalent forms)