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 use \((0,6)\) and \((7,0)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute \(x_1 = 0,y_1 = 6,x_2 = 7,y_2 = 0\) into the formula:
\(m=\frac{0 - 6}{7 - 0}=\frac{-6}{7}\)

Step4: Write the equation

Substitute \(m =-\frac{6}{7}\) and \(b = 6\) into \(y=mx + b\).
We get \(y=-\frac{6}{7}x + 6\)

Answer:

\(y = -\frac{6}{7}x + 6\)