Question

h the point with the given slope.

1. (-8, 6); slope = \\(\frac{1}{4}\\)

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)\) is a point on the line and \(m\) is the slope of the line. Here, \(x_1=-8\), \(y_1 = 6\) and \(m=\frac{1}{4}\).

Step2: Substitute values into point - slope form

Substitute \(x_1=-8\), \(y_1 = 6\) and \(m=\frac{1}{4}\) into the formula \(y - y_1=m(x - x_1)\):
\(y-6=\frac{1}{4}(x - (-8))\)
Simplify the right - hand side: \(y - 6=\frac{1}{4}(x + 8)\)

Step3: Distribute and simplify to slope - intercept form (optional, but for clarity)

Distribute \(\frac{1}{4}\) on the right - hand side: \(y-6=\frac{1}{4}x+2\)
Add 6 to both sides of the equation: \(y=\frac{1}{4}x+2 + 6\)
So, \(y=\frac{1}{4}x+8\)

If the problem is to find the equation of the line passing through the point \((-8,6)\) with slope \(\frac{1}{4}\), the equation is \(y=\frac{1}{4}x + 8\) (or in point - slope form \(y - 6=\frac{1}{4}(x + 8)\)).

Answer:

The equation of the line is \(y=\frac{1}{4}x + 8\) (or \(y-6=\frac{1}{4}(x + 8)\))