Line Equation with angle?

Question

How can I find equation of a line or draw a line, given a starting point, length of line and angle of line (relative to x-axis)?

Answer 1

To find the equation using trig:

Using trig you can find the slope of the line by drawing a triangle with the x-axis tanθ=opp/adj and if you mark those you can also see that the opposite of the angle is the rise and the adjacent is the run of your line so the slope of the line is equal to tangent of the angle it makes relative to the x-axis

m=tanθ (where theta is the angle to the horizontal/x-axis)

then you can either use the starting point of the line or another point on the line to write the equation in point slope form

y-y₁=m(x-x₁)

Or find the y-intercept and write the equation in slope intercept form

y=mx+b

then draw the line to your desired length

Draw the line with a protractor and a ruler

Starting from your starting point draw a horizontal line to measure the angle from (if your starting point is on the x-axis or you are using grid paper this step isn't needed). Use the protractor to make a point at the appropriate angle above or below the horizontal and then use your ruler to measure the length desired and then draw the line. Because all horizontal lines are parallel to each other the angle your line makes with the x-axis is the angle it makes with any horizontal line.

From there if you want to write the equation you can measure the change in y and x using your ruler and find the slope and then using either point slope or slope intercept form write the equation of the line.