Question

Consider the graph of the line y = .5x- 4 and the point

Answer 1

Answer:

slope of parallel line and perpendicular line are 5 and -1/5 espectively

equation of parallel and perpendicular line are y = 5x + 22 $y= \frac{-1}{5} x+\frac{6}{5}$ respectively

Step-by-step explanation:

y = 5x - 4 is in the form

y = mx + c

where m is the slope of the line and c is the y intercept of thr line

therefore slope of the line = 5 and y intercept = -4

when an another line is parallel to the given line then the slope of both the lines are equal

therefore the slope the parallel line = 5

equation of a line passing through a given point $(x_{1} ,y_{1})$ with slope m is given by $y-y_{1} = m(x-x_{1} )$

given $(x_{1} ,y_{1})$= (-4,2)

therefore equation of line y-2 = 5(x+4)

therefore y = 2+ 5x+20

y = 5x + 22is the eqaution of required line.

when two lines are perpendiculer then

$m_{1} m_{2}=-1$

where $m_{1} and m_{2}$ are slope of the lines therefore

m×5=-1

therefore m= $\frac{-1}{5}$

therefore eqaution of line passing through (-4,2) and with slope m= $\frac{-1}{5}$ is given by $y - 2= \frac{-1}{5} (x+4)$

$y= \frac{-1}{5} x+\frac{6}{5}$