Question

write the equation of line that passes through the point (-3, 1) and has a slope of -2

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, \(x_1=- 3\), \(y_1 = 1\) and \(m=-2\).

Step2: Substitute values into point - slope form

Substitute \(x_1=-3\), \(y_1 = 1\) and \(m = - 2\) into the point - slope formula:
\(y-1=-2(x - (-3))\)
Simplify the equation:
\(y - 1=-2(x + 3)\)

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

Expand the right - hand side: \(y-1=-2x-6\)
Add 1 to both sides of the equation:
\(y=-2x-6 + 1\)
\(y=-2x-5\)
We can also write it in standard form \(Ax+By = C\) (where \(A\), \(B\), \(C\) are integers and \(A\geq0\)):
\(2x+y=-5\)

Answer:

The equation of the line in slope - intercept form is \(y=-2x - 5\) (or in standard form \(2x + y=-5\))