Question

the graph of a line is shown on the coordinate plane below.
the graph of a line is shown on the coordinate plane below.
graph of a line on a coordinate plane with x-axis from -6 to 6 and y-axis from -6 to 6, line passes through (0,1) and other points
which equation represents the graph of the line?
a ( y = \frac{1}{2}x + 1 )
b ( y = \frac{1}{2}x - 2 )
c ( y = 2x + 1 )
d ( y = 2x - 2 )

Explanation:

Step1: Identify y-intercept

The line crosses the y - axis at (0, 1), so the y - intercept \(b = 1\). This eliminates options B (\(y=\frac{1}{2}x - 2\), \(b=-2\)) and D (\(y = 2x-2\), \(b = - 2\)).

Step2: Calculate slope

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

Step3: Form equation

The slope - intercept form is \(y=mx + b\). With \(m=\frac{1}{2}\) and \(b = 1\), the equation is \(y=\frac{1}{2}x+1\), which is option A.

Answer:

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