Question

what is the equation of the line that passes through the point (5, 8) and has a slope of \\(\frac{2}{5}\\)?

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, $x_1 = 5$, $y_1=8$ and $m=\frac{2}{5}$.

Step2: Substitute values into point - slope form

Substitute $x_1 = 5$, $y_1 = 8$ and $m=\frac{2}{5}$ into the point - slope formula:
$y-8=\frac{2}{5}(x - 5)$

Step3: Simplify the equation

First, distribute $\frac{2}{5}$ on the right - hand side:
$y-8=\frac{2}{5}x-2$
Then, add 8 to both sides of the equation to solve for $y$:
$y=\frac{2}{5}x-2 + 8$
$y=\frac{2}{5}x+6$

Answer:

The equation of the line is $y=\frac{2}{5}x + 6$