Question

Consider the line y=9x -2.Find the equation of the line that is parallel to this line and passes through the point (-6, 6).Find the equation of the line that is perpendicular to this line and passes through the point (-6,6)

Answer 1

hello

the question presented here deals with equation of a line passing through one point

to know that, we need to know two things

1. slope

2. intercept

y = mx+c

m = slope

c = intercept

but the line passes through point (-6,6)

now to find the new equation,

y = mx + c

y = 9x + c

but it passes through (-6,6)

x= -6, y= 6

now let's plug in the values into the equation to find the intercept c

`\begin{gathered} y=mx+c \\ 6=9(-6)+c \\ 6=-54+c \\ \text{solve for c} \\ c=6+54 \\ c=60 \end{gathered}`

now that we've found c, we can plug it into our equation of straight line

y = 9x + 60

the equation of the line for it passes through points (-6,6) is y = 9x +60