# Graphing Calculator Drawing: Slanted Lines

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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.

\begin{align*} y&=10x \\[10pt] y&=1x \\[10pt] y&=0.1x \\[10pt] y&=0x \\[10pt] y&=-0.1x \\[10pt] y&=-1x \\[10pt] y&=-10x \end{align*}

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 $(0,b).$

\begin{align*} y&=x+5 \\[10pt] y&=x+2 \\[10pt] y&=x+1 \\[10pt] y&=x+0 \\[10pt] y&=x-1 \\[10pt] y&=x-2 \\[10pt] y&=x-5 \end{align*}

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 part of a series.

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