Question

write an equation of the line.

Explanation:

Step1: Find the slope (m)

We use two points \((x_1,y_1)=(4,3)\) and \((x_2,y_2)=(9, - 2)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
\[m=\frac{-2 - 3}{9 - 4}=\frac{-5}{5}=- 1\]

Step2: Find the y - intercept (b)

We know the line passes through \((0,7)\) (from the y - axis intercept in the graph). So when \(x = 0\), \(y=b = 7\).

Step3: Write the equation

The slope - intercept form of a line is \(y=mx + b\). Substituting \(m=-1\) and \(b = 7\), we get \(y=-x + 7\).

Answer:

\(y=-x + 7\)