Question

what is the equation of the line that passes through the point (-3, 6) and has a slope of -4?

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, \(x_1=-3\), \(y_1 = 6\) and \(m=-4\).

Step2: Substitute values into point - slope form

Substitute \(x_1=-3\), \(y_1 = 6\) and \(m = - 4\) into the point - slope formula:
\(y-6=-4(x - (-3))\)
Simplify the right - hand side: \(y - 6=-4(x + 3)\)

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

Expand the right - hand side: \(y-6=-4x-12\)
Add 6 to both sides of the equation: \(y=-4x-12 + 6\)
Simplify the right - hand side: \(y=-4x-6\)
We can also write it in standard form \(Ax+By = C\) (where \(A\), \(B\), and \(C\) are integers and \(A\geq0\)):
\(4x+y=-6\) (by adding \(4x\) to both sides of \(y=-4x - 6\))

Answer:

The equation of the line is \(y=-4x - 6\) (or \(4x + y=-6\))