Question

slope intercept form
write the equation for the line.
y = mx + b
graph of a line
y = □x + □

Explanation:

Step1: Find the y-intercept (b)

The y-intercept is the value of y when x = 0. From the graph, the line crosses the y-axis at (0, 1), so \( b = 1 \).

Step2: Calculate the slope (m)

We can use two points on the line, e.g., (0, 1) and (1, 3). The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Substituting the points: \( m=\frac{3 - 1}{1 - 0}=\frac{2}{1}=2 \).

Step3: Write the equation

Using the slope-intercept form \( y = mx + b \), substitute \( m = 2 \) and \( b = 1 \), so the equation is \( y = 2x + 1 \).

Answer:

\( y = \boldsymbol{2}x + \boldsymbol{1} \)