A table titled Angle Measure Conversion with two columns and seven rows. The first column, Degrees, has the entries negative 180, negative 90, 0, 90, 180, 270. The second column, Gradients, has the entries, negative 200, negative 100, 0, 100, 200, 300.
Engineers measure angles in gradients, which are smaller than degrees. The table shows the conversion of some angle measures in degrees to angles in gradients. What is the slope of the line representing the conversion of degrees to gradients?

Express your answer as a decimal rounded to the nearest hundredth.

We can also find the slope of a line by using any two points (x, y) and (x, y) on the line, using the formula for slope m = (y - y)/(x - x).

How do we solve the given question?

In the question, we are given a table with readings of degrees and gradients converted from the degrees.

We are asked to find the slope of the line representing the conversion from degrees to gradients.

We take degrees on the x-axis and gradients on the y-axis, mark the points, and draw the trendline. (Check the attachment)

Now, to find the slope of this line, we take the point (-180, -200) as (x, y) and (270, 300) as (x, y).

Using the formula for slope m = (y - y)/(x - x), we find the slope of this line,

m = (300 - (-200))/(270 - (-180)) = (300 + 200)/(270 + 180) = 500/450 = 10/9.

Taking the slope in decimal form, rounded to the nearest hundredth, we get, m = 10/9 = 1.11.

∴ The slope of the line representing the conversion of degrees to gradients is 1.11.

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