Question

intro to slope intercept form assessment
13 of 17
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 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 the y - intercept $(0,4)$ and another point, say $(4,3)$ (by looking at the graph, when $x = 4$, $y = 3$). The formula for slope is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using $(x_1,y_1)=(0,4)$ and $(x_2,y_2)=(4,3)$, we get $m=\frac{3 - 4}{4 - 0}=\frac{- 1}{4}=-\frac{1}{4}$.

Step4: Write the equation

Substitute $m = -\frac{1}{4}$ and $b = 4$ into $y=mx + b$. So the equation is $y=-\frac{1}{4}x + 4$.

Answer:

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