Question

write an equation in point - slope form for the line that satisfies the given set of conditions. slope of \\(\frac{4}{5}\\), passes through \\((10, - 3)\\)

Explanation:

Step1: Recall point - slope formula

The point - slope form of a linear equation is given by \(y - y_1=m(x - x_1)\), where \(m\) is the slope of the line and \((x_1,y_1)\) is a point that the line passes through.

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

We are given that the slope \(m = \frac{4}{5}\) and the line passes through the point \((10,- 3)\). So, \(x_1 = 10\) and \(y_1=-3\).

Step3: Substitute values into the formula

Substitute \(m=\frac{4}{5}\), \(x_1 = 10\) and \(y_1=-3\) into the point - slope formula \(y - y_1=m(x - x_1)\).
We get \(y-(-3)=\frac{4}{5}(x - 10)\), which simplifies to \(y + 3=\frac{4}{5}(x - 10)\).

Answer:

\(y + 3=\frac{4}{5}(x - 10)\)