Respuesta :

let's start by simply using two points from the line hmmmmm wait a second, low and behold, there are two there already labeled, so, let's use those ones then,

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 0}}\quad ,&{{ 7}})\quad % (c,d) &({{ 8}}\quad ,&{{ -2}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-2-7}{8-0}\implies \cfrac{-9}{8}[/tex]

[tex]\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-7=-\cfrac{9}{8}(x-0)\implies y-7=-\cfrac{9}{8}x \\\\\\ y=-\cfrac{9}{8}x+7[/tex]
calculista

Answer:

[tex]y=-\frac{9}{8}x+7[/tex]

Step-by-step explanation:

we know that

The equation of the line into slope intercept form is equal to

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

where

m is the slope

b is the y-coordinate of the y-intercept

In this problem we have

[tex]b=7[/tex] ------> because the point [tex](0,7)[/tex] is the y-intercept

point [tex](8,-2)[/tex]

substitute the value of x , y and b in the equation to solve for m

[tex]y=mx+b[/tex]------> [tex]-2=m(8)+7[/tex]

[tex]m(8)=-2-7[/tex]

[tex]m=-9/8[/tex]

therefore

the equation is equal to

[tex]y=-\frac{9}{8}x+7[/tex]


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