Question

find the slope - intercept equation of the line that has the given characteristics. slope (-\frac{13}{9}) and y - intercept ((0, - 3)) the slope - intercept equation is (-\frac{13}{9}x - 0). (type an equation. type your answer in slope - intercept form. use integers or fractions for any numbers)

Explanation:

Step1: Recall slope-intercept form

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step2: Substitute given slope

Substitute $m = -\frac{13}{9}$ into the formula: $y = -\frac{13}{9}x + b$

Step3: Substitute y-intercept value

The y-intercept is $(0, -3)$, so $b = -3$. Substitute this into the equation: $y = -\frac{13}{9}x + (-3)$

Step4: Simplify the equation

Rewrite the equation to simplify the constant term: $y = -\frac{13}{9}x - 3$

Answer:

$y = -\frac{13}{9}x - 3$