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What is equation of the line graphed below?

What Is Equation Of The Line Graphed Below class=

Sagot :

kaylenxc
using the parent function y = mx + b,
y = -3x
slope is m- so rise over run -3/1 = -3
where the line crosses the y axis is b- 0 (origin)
VectorFundament120

Explanation

  • Find the slope by using rise over run with two coordinate points.

[tex](0,0) \longrightarrow \sf{part \: \: of \: \: the \: \: graph} \\ (1, - 3)\longrightarrow \sf{given \: \:coordinate \: \: point}[/tex]

[tex]m = \frac{dy}{dx} = \frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute these coordinate values in.

[tex]m = \frac{0 - ( - 3)}{0 - 1} \\ m = \frac{3}{ - 1} \\ m = - 3[/tex]

Hence, the slope is -3.

  • Find the y-intercept.

From the graph, the line passes through the origin point. Therefore, the y-intercept is (0,0).

  • Slope-Intercept form

[tex]y = mx + b \\ \begin{cases} \sf{m = slope} \\ \sf{b = y - intercept} \end{cases}[/tex]

Substitute both m and b in the slope-intercept form.

[tex]y = - 3x + 0 \\ y = - 3x[/tex]

Hence the answer is y = -3x.

Answer

[tex] \large \boxed{y = - 3x}[/tex]

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