Question 1 What is the name given to the line that is collinear and contains the three centers of
triangle?

The line y = x
The x-axis
The Isosceles Line
The y-axis
The Pascal Line
The Euler Line

Explanation:

The Euler Line contains the following points

all of which can be thought of as the "center" of a triangle. Strangely enough, the incenter is not generally found on the Euler line.

Step-by-step explanation:

Linear equations are typically organized in slope-intercept form: . Here's what the variables mean:

y = the y-coordinate

m = the slope

x = the x=coordinate

b = the y-intercept (what y is equal to when the line crosses the y-axis)

First, we need to calculate the slope of the line (m). The slope is the of the line, or in other words, the change in y over the change in x. We can find this by just looking at the graph, between the two given points. For 3 spaces the line travels to the right, it travels downward 2 spaces. Therefore, the slope of the line is .

We can also calculate this using the formula by using two points that fall on the line, and . Here, we can use the points (-3,3) and (0,1).

Two negatives make a positive

Then, we need to find the y-intercept of the line (b). We can find this by, again, looking at the graph. The line crosses the y-axis when y is equal to 1, so the y-intercept of the line is 1.

Now, we plug our calculated values back into the original equation:

I hope this helps!