Question

use the given conditions to write an equation for the line in point - slope form and in slope - intercept form.\
slope = \\(\frac{4}{5}\\), passing through the origin\
write an equation for the line in point - slope form.\
(simplify your answer. use integers or fractions for any numbers in the equation.)\
write an equation for the line in slope - intercept form.\
(simplify your answer. use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Recall point-slope formula

The point-slope form of a line is $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is a point on the line. The origin is $(0,0)$, and $m=\frac{4}{5}$.

Step2: Substitute values into point-slope

Substitute $m=\frac{4}{5}$, $x_1=0$, $y_1=0$:
$y - 0 = \frac{4}{5}(x - 0)$
Simplify to get the point-slope form.

Step3: Convert to slope-intercept form

Slope-intercept form is $y = mx + b$, where $b$ is the y-intercept. Since the line passes through the origin, $b=0$. Substitute $m=\frac{4}{5}$ and $b=0$:
$y = \frac{4}{5}x + 0$
Simplify to get the slope-intercept form.

Answer:

Point-slope form: $y = \frac{4}{5}x$
Slope-intercept form: $y = \frac{4}{5}x$