Question

write the equation of this line in slope - intercept 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 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 the y - intercept \((0,6)\) and another point, say \((- 8,1)\) (from the left end of the line). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute \(x_1 = 0,y_1 = 6,x_2=-8,y_2 = 1\) into the formula:
\(m=\frac{1 - 6}{-8-0}=\frac{-5}{-8}=\frac{5}{8}\)? Wait, no, let's check another point. Wait, when \(x = 2\), \(y = 7\) (from the graph: when \(x = 2\), \(y\) is 7). So using \((0,6)\) and \((2,7)\):
\(m=\frac{7 - 6}{2-0}=\frac{1}{2}\). Ah, that's better. Let's verify with \((0,6)\) and \((-2,5)\): \(\frac{5 - 6}{-2 - 0}=\frac{-1}{-2}=\frac{1}{2}\). Yes, so the slope \(m=\frac{1}{2}\).

Step4: Write the equation

Substitute \(m=\frac{1}{2}\) and \(b = 6\) into \(y=mx + b\).
We get \(y=\frac{1}{2}x+6\).

Answer:

\(y=\frac{1}{2}x + 6\)