I've been given a graph and must identify the slope.

Question

I have been given a question/problem where there is a graph that is not labeled (no numbers on y or x axis). The x axis is labeled "n" and there is what looks like the y axis but i'm not sure because its not directly on one of the gird lines and the line is dashed, but that line is labeled "m". There is a line that goes through both "n" and "m" and the angle that is made from when this line meets the x axis/"n" makes an angle of 36 degrees. the line never directly goes through a point either. slope is y=mx+b but i'm not sure how I'm suppose to solve this as we haven't talked about slope since last year (in algebra 1)

Answer 1

If the graph has no axis numbers and the line doesn't pass through clear points, then you can't use rise / run which is counting the number of units you go up / down and left / right from one point to another on a line. Though they did give you the angle the line meets the x-axis which is 36° and that would be enough to find the slope using trigonometry.

When a line makes an angle θ with the positive x-axis:

slope = tan θ and here θ = 36° so we solve:

slope = tan 36°

slope = 0.7265

Therefore, the slope of the line is approximately 0.73.

Answer 2

Slope is change in y divided by change in x. Change in x is the sine of the angle and change in y is the cosine.