Respuesta :

Explanation

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

[tex]\begin{cases} (x_1,y_1)=(-3,4) \\ (x_2,y_2)=(2,8) \end{cases} \\ m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]

  • Substitute the coordinate values in.

[tex]m = \frac{8 - 4}{2 - ( - 3)} \\ m = \frac{4}{2 + 3} \Longrightarrow \frac{4}{5} [/tex]

We have got the value of slope. Substitute in the slope-intercept form.

  • Slope-Intercept

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

Substitute and Rewrite the equation.

[tex]y = \frac{4}{5} x + b[/tex]

  • Find the y-intercept or the value of b by substituting any given coordinate points.

I will substitute (2,8) in.

[tex]y = \frac{4}{5} x + b \Longrightarrow \sf \small{Substitute \: \: the \: \: coordinate \: \: points \: \: in \: \: the \: \: equation}[/tex]

[tex]8 = \frac{4}{5} (2) + b \\ 8 = \frac{8}{5} + b \\ 40 = 8 + 5b \\ 40 - 8 = 5b \\ 32 = 5b \\ \frac{32}{5} = b[/tex]

Rewrite the equation by substituting the value of b.

[tex]y = \frac{4}{5} x + \frac{32}{5} [/tex]

Answer

[tex] \large \boxed{y = \frac{4}{5} x + \frac{32}{5} }[/tex]

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