Question

a line passes through the point (-8, 5) and has a slope of \\(\frac{5}{4}\\). write an equation in point - slope form for this line.

Explanation:

Step1: Recall point - slope formula

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.

Step2: Identify values of \(x_1\), \(y_1\) and \(m\)

We are given that the line passes through the point \((-8,5)\), so \(x_1=-8\) and \(y_1 = 5\). The slope \(m=\frac{5}{4}\).

Step3: Substitute values into the formula

Substitute \(x_1=-8\), \(y_1 = 5\) and \(m=\frac{5}{4}\) into the point - slope formula \(y - y_1=m(x - x_1)\).
We get \(y - 5=\frac{5}{4}(x-(-8))\), which simplifies to \(y - 5=\frac{5}{4}(x + 8)\).

Answer:

\(y - 5=\frac{5}{4}(x + 8)\)