Question

1. write the equation of the line in slope - intercept form.

Explanation:

Step1: Recall 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.

Step2: Find the y - intercept ($b$)

The y - intercept is the value of $y$ when $x = 0$. From the point $(0,3)$, we can see that when $x = 0$, $y=3$. So, $b = 3$.

Step3: Calculate the slope ($m$)

The formula for the slope between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. We have the points $(0,3)$ (so $x_1 = 0,y_1 = 3$) and $(4,2)$ (so $x_2=4,y_2 = 2$).
Substitute into the slope formula: $m=\frac{2 - 3}{4 - 0}=\frac{- 1}{4}=-\frac{1}{4}$.

Step4: Write the equation

Substitute $m =-\frac{1}{4}$ and $b = 3$ into the slope - intercept form $y=mx + b$. We get $y=-\frac{1}{4}x + 3$.

Answer:

$y =-\frac{1}{4}x + 3$