Question

write the equation of this line in slope - intercept form.
write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Identify slope-intercept form

Slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Find the y - intercept ($b$)

The line crosses the y - axis at $(0, - 5)$, so $b=-5$.

Step3: Calculate the slope ($m$)

We can use two points on the line. Let's take the y - intercept $(0, - 5)$ and another point, say $(2,1)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Substitute $x_1 = 0,y_1=-5,x_2 = 2,y_2 = 1$ into the formula:
$m=\frac{1-(-5)}{2 - 0}=\frac{1 + 5}{2}=\frac{6}{2}=3$

Step4: Write the equation

Substitute $m = 3$ and $b=-5$ into $y=mx + b$:
$y=3x-5$

Answer:

$y = 3x-5$