An illustration of a scatterplot graph shows x-axis ranging from 0 to 10 in increments of 1 and y-axis ranging from 0 to 50 in increments of 10. Multiple points are plotted around a line that points downward to the right with an arrowhead on the bottom.

Question

The line passes approximately through left parenthesis 0 comma 45 right parenthesis, left parenthesis 2 comma 25 right parenthesis, left parenthesis 3 comma 15 right parenthesis, and left parenthesis 4.5 comma 0 right parenthesis. 13 points are plotted close to the line.
Write an equation in slope-intercept form of the trend line.

(1 point)
y=
x +

Answer 1

To find the equation of the trend line in slope-intercept form $y=mx+b$, we first need to determine the slope $m$ and the y-intercept $b$.

From the points you provided, we can calculate the slope $m$ using the following formula:

$$m=\frac{y_2-y_1}{x_2-x_1}$$

Using the points $(0,45)$ and $(4.5,0)$:

$$x_1=0,y_1=45$$ $$x_2=4.5,y_2=0$$

Calculating the slope:

$$m=\frac{0-45}{4.5-0}=\frac{-45}{4.5}=-10$$

Now, we can use one of the points to find the y-intercept $b$. We'll use the point $(0,45)$:

Using the slope-intercept form:

$$y=mx+b$$

At $x=0$:

$$45=-10(0)+b$$

This simplifies to:

$$b=45$$

Putting this all together, the equation of the trend line is:

$$y=-10x+45$$

So, in summary:

$y=-10x+45$