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: 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: Find the y - intercept (\(b\))

The y - intercept is the point where the line crosses the y - axis. From the graph, the line crosses the y - axis at \((0,6)\), so \(b = 6\).

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

The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). We can use two points on the line. We know the y - intercept \((0,6)\) and the x - intercept \((7,0)\) (where the line crosses the x - axis).
Using the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\) with \((x_1,y_1)=(0,6)\) and \((x_2,y_2)=(7,0)\):
\(m=\frac{0 - 6}{7 - 0}=\frac{-6}{7}\)

Step4: Write the equation

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

Answer:

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