Question

write the equation of the line in fully simplified slope-intercept form.
answer attempt 1 out of 2
answer:
submit answer

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, 4)\) (the y - intercept) and \((6, 5)\).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,4)\) and \((x_2,y_2)=(6,5)\). Then \(m=\frac{5 - 4}{6 - 0}=\frac{1}{6}\).

Step3: Write the equation in 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. We know that \(m=\frac{1}{6}\) and \(b = 4\) (since the line crosses the y - axis at \((0,4)\)). So the equation of the line is \(y=\frac{1}{6}x + 4\).

Answer:

\(y=\frac{1}{6}x + 4\)