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SLOPE

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1.) Find the slope of the line containing the points (-4, 1) and (2, 3).

[tex]\sf m = \frac{rise}{run} = \frac{y_2 \: - \: y_1}{x_2 \: - \: x_1} [/tex]

[tex]\sf m = \frac{3 \: - \: 1}{2 \: - \: (- 4)} [/tex]

[tex]\sf m = \frac{2}{ 6} [/tex]

[tex]\sf m = \frac{1}{3} [/tex]

↬ Hence, the slope of the line is 1/3

2.) Tell whether the line through (0, 3) and (5, -5) rises, falls, is horizontal, or is vertical.

First, find the slope

[tex]\sf m = \frac{rise}{run} = \frac{y_2 \: - \: y_1}{x_2 \: - \: x_1} [/tex]

[tex]\sf m = \frac{( - 5) \: - \: 3}{5 \: - \: 0} [/tex]

[tex]\sf m = \frac{ - 8}{5} [/tex]

[tex]\sf m = - \frac{8}{5} [/tex]

Second, find the y-intercept

[tex]\sf b = y_1 - mx_1[/tex]

[tex]\sf b = (3) - \cancel{( - \frac{8}{5} )(0)}[/tex]

[tex]\sf b = 3[/tex]

Finally, write an equation in the form y = mx + b using the values that we got.

[tex]\sf y = mx + b[/tex]

[tex]\sf y = - \frac{8}{5} x + 3[/tex]

↬ Since the slope is negative the line falls.

Note:

• positive slope = the line rises
• negative slope = the line falls
• undefined = the line is vertical
• zero = the line is horizontal

Answer:

[tex]\huge\boxed{\begin{cases} \sf{Slope=1/3}\\\sf{The\:line\:falls}\end{cases}}[/tex]

Step-by-step explanation:

• Use the literal equation below to find the slope:

[tex]\sf{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Where:

[tex]\bullet\quad\sf{y_2=the\:y-coordinate\:of\:the\:second\:point\:=3}[/tex]

[tex]\bullet\quad\sf{x_2=the\:x-coordinate\:of\:the\:second\:point = 2}[/tex]

[tex]\bullet\quad\sf{y_1=the\:y-coordinate\:of\:the\:first\:point=1}[/tex]

[tex]\bullet\quad\sf{x_1 =the\:x-coordinate\:of\:the\:first\:point=-4}[/tex]

Put the values:

[tex]\sf{m=\dfrac{3-1}{2-(-4)}}[/tex]

[tex]\sf{m=\dfrac{2}{2+4}}[/tex]

[tex]\sf{m=\dfrac{2}{6}}[/tex]

[tex]\sf{m=\dfrac{1}{3}}[/tex]

Question 2

• Once again, use the equation & find the slope:

[tex]\sf{m=\dfrac{-5-3}{5-0}}[/tex]

[tex]\sf{m=\dfrac{-8}{5}}[/tex]

[tex]\rm{\Uparrow\:Notice\:that\:the\:slope\:is\:negative,\:this\:means\;the\;line\;falls}[/tex]

~ SN 180

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Don't hesitate to reach out to me if you have any queries.

Best wishes!

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