Question

What is the equation of this graphed line?

Answer 1

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,

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

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

Answer 2

Answer:

$y=-\frac{9}{8}x+7$

Step-by-step explanation:

we know that

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

$y=mx+b$

where

m is the slope

b is the y-coordinate of the y-intercept

In this problem we have

$b=7$ ------> because the point $(0,7)$ is the y-intercept

point $(8,-2)$

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

$y=mx+b$------> $-2=m(8)+7$

$m(8)=-2-7$

$m=-9/8$

therefore

the equation is equal to

$y=-\frac{9}{8}x+7$