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 \( (0,-6) \), so \( b=-6 \).

Step3: Calculate the slope (\( m \))

We can use two points on the line. Let's take \( (0, - 6) \) and \( (18,0) \). The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Substitute \( x_1 = 0,y_1=-6,x_2 = 18,y_2 = 0 \) into the formula: \( m=\frac{0-(-6)}{18 - 0}=\frac{6}{18}=\frac{1}{3} \).

Step4: Write the equation

Substitute \( m=\frac{1}{3} \) and \( b = - 6 \) into \( y=mx + b \). We get \( y=\frac{1}{3}x-6 \).

Answer:

\( y=\frac{1}{3}x - 6 \)