Question

write the equation of the line in fully simplified 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 \((0,1)\), so \(b = 1\).

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

Use two points, e.g., \((0,1)\) and \((1,2)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute \(x_1 = 0,y_1 = 1,x_2 = 1,y_2 = 2\) into the formula: \(m=\frac{2 - 1}{1 - 0}=\frac{1}{1}=1\).

Step4: Write the equation

Substitute \(m = 1\) and \(b = 1\) into \(y=mx + b\), we get \(y=x + 1\).

Answer:

\(y = x+1\)