Question

question
what is the equation of the line that passes through the point (3, -8) and has a slope of -1?

Explanation:

Step1: Recall point - slope form

The point - slope form of a line 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, \(x_1 = 3\), \(y_1=-8\) and \(m=-1\).

Step2: Substitute values into point - slope form

Substitute \(x_1 = 3\), \(y_1=-8\) and \(m = - 1\) into the point - slope formula:
\(y-(-8)=-1(x - 3)\)
Simplify the left - hand side: \(y + 8=-1(x - 3)\)

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

Expand the right - hand side: \(y+8=-x + 3\)
Subtract 8 from both sides: \(y=-x+3 - 8\)
Simplify the right - hand side: \(y=-x - 5\)
We can also write it in the standard form \(x+y=-5\) (by adding \(x\) to both sides of \(y=-x - 5\))

Answer:

The equation of the line is \(y=-x - 5\) (or \(x + y=-5\))