Question

q. write the equation of the line in slope - intercept 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 \((0,7)\), so \(b = 7\).

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

We can use two points on the line, e.g., \((0,7)\) and \((1,5)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting the points \((x_1,y_1)=(0,7)\) and \((x_2,y_2)=(1,5)\) into the formula:
\(m=\frac{5 - 7}{1 - 0}=\frac{- 2}{1}=-2\)

Step4: Write the equation

Substitute \(m=-2\) and \(b = 7\) into \(y=mx + b\).
We get \(y=-2x + 7\)

Answer:

\(y=-2x + 7\)