Question

a line passes through the point (8, 6) and has a slope of \\(\frac{5}{4}\\). write an equation in slope-intercept form for this line.

Explanation:

Step1: Recall point - slope form

The point - slope form of a line 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. We know that $m = \frac{5}{4}$ and the point $(x_1,y_1)=(8,6)$. Substitute these values into the point - slope form:
$y - 6=\frac{5}{4}(x - 8)$

Step2: Simplify to slope - intercept form

The slope - intercept form is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. We simplify the equation from step 1:
First, distribute $\frac{5}{4}$ on the right - hand side:
$y - 6=\frac{5}{4}x-\frac{5}{4}\times8$
$\frac{5}{4}\times8 = 10$, so the equation becomes:
$y - 6=\frac{5}{4}x-10$
Then, add 6 to both sides of the equation to solve for $y$:
$y=\frac{5}{4}x-10 + 6$
$y=\frac{5}{4}x-4$

Answer:

$y=\frac{5}{4}x - 4$