# Graphing Calculator Drawing: Slanted Lines

*Slanted lines can be used to draw a spider web.*

*This post is a chapter in the book Graphing Calculator Drawing Exercises.* *Suggested citation:* Skycak, J. (2019). Graphing Calculator Drawing: Slanted Lines. *Graphing Calculator Drawing Exercises.* https://justinmath.com/graphing-calculator-drawing-slanted-lines/

** Setup.** Navigate to https://www.desmos.com/calculator. Be sure to sign in so that you can save your graph.

** Demonstration - Slope.** Observe the graph as you type each of the following inputs. In general, the line $y=mx$ goes $m$ units up per unit it goes right.

** Demonstration - Intercept.** Observe the graph as you type each of the following inputs. In general, the graph $y=mx+b$ crosses the y-axis at the point $(0,b).$

** Exercise.** Draw the two lines shown below. (Hint: one of the lines is given by $y=1-\frac{1}{9}x.$)

** Exercise.** Draw more lines to reproduce the “spider web” graph shown below.

** Exercise.** Draw more lines to reflect the spider web upwards. (Hint: starting with the lines you drew previously, you can make the slopes positive, and adjust the intercepts as needed.)

** Demonstration.** The equation $y=m(x-a)+b$ creates a line with slope $m$ through the point $(a,b).$

- The line through $(9,0)$ with slope $\frac{1}{9}$ is given by $y=\frac{1}{9}(x-9)+0.$
- The line through $(10,0)$ with slope $\frac{2}{8}$ is given by $y=\frac{2}{8}(x-9)+0.$

** Exercise.** Draw more lines to complete the bottom-right portion of your spider web. Two of the lines are given in the previous demonstration.

** Exercise.** Using the equation $y=m(x-a)+b,$ complete the top-right corner of your spider web. Two lines are provided below.

- The line through $(18,17)$ with slope $-\frac{1}{9}$ is given by $y=-\frac{1}{9}(x-18)+17.$
- The line through $(18,16)$ with slope $-\frac{2}{8}$ is given by $y=-\frac{2}{8}(x-18)+16.$

*This post is a chapter in the book Graphing Calculator Drawing Exercises.* *Suggested citation:* Skycak, J. (2019). Graphing Calculator Drawing: Slanted Lines. *Graphing Calculator Drawing Exercises.* https://justinmath.com/graphing-calculator-drawing-slanted-lines/