Question

(a) Graph the line through the points (-6,4) and (6,-8).-10-86422N4 68 i10 -8 -6 -4 -2-2-4-6-810-Clear All Draw:FAN(b) Write an equation of the line in the form y = mx + b.y =

Answer 1

Graph the line through the points (-6,4) and (6,-8):

(a) when x = -6 , y = 4 and x = 6 , y = -8

(b) Write an equation of a line in the form y = mx+b

`\begin{gathered} (y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1) \\ (-6,4)\longrightarrow x_1=-6,y_1=4 \\ (6,-8)\longrightarrow x_2=6,y_2=-8 \end{gathered}`
`\begin{gathered} (y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1) \\ \frac{y-4}{x--6_{}}=(-8-4)/(6--6) \\ (y-4)/(x+6)=-(12)/(6+6) \\ (y-4)/(x+6)=-(12)/(12) \\ (y-4)/(x+6)=-1 \\ \text{cross multiply} \\ y-4=-1(x+6) \\ y-4=-x-6 \\ \text{add 4 to both side } \\ y-4+4=-x-6+4 \\ y=-x-2 \end{gathered}`

Therefore the equation of the line is y = -x -2