Question

1. write the equation of the line shown on the grid 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 point where the line crosses the y - axis. From the graph, the line crosses the y - axis at $(0,4)$, so $b = 4$.

Step3: Calculate the slope ($m$)

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. We can use two points on the line. Let's use the y - intercept $(0,4)$ and another point, say $(3,6)$ (we can find this by moving 3 units to the right and 2 units up from the y - intercept).
Substitute $x_1 = 0,y_1 = 4,x_2 = 3,y_2 = 6$ into the slope formula:
$m=\frac{6 - 4}{3 - 0}=\frac{2}{3}$

Step4: Write the equation

Substitute $m=\frac{2}{3}$ and $b = 4$ into the slope - intercept form $y=mx + b$.
We get $y=\frac{2}{3}x + 4$

Answer:

$y=\frac{2}{3}x + 4$