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 \( (0,4) \), so \( b = 4 \).

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

We can use two points on the line. Let's take \( (- 10,0) \) and \( (0,4) \). The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Substituting \( x_1=-10,y_1 = 0,x_2 = 0,y_2 = 4 \) into the formula: \( m=\frac{4 - 0}{0-(-10)}=\frac{4}{10}=\frac{2}{5} \).

Step4: Write the equation

Substitute \( m=\frac{2}{5} \) and \( b = 4 \) into \( y=mx + b \). We get \( y=\frac{2}{5}x+4 \).

Answer:

\( y=\frac{2}{5}x + 4 \)