Question

Rewrite each equation in slope-intercept form, if necessary, then determine whether the lines are parallel , perpendicular, or neither.A.)y=1\3x+4B.) 3x+y=2 The slope A is The slope B is Lines A and B are These are the option choices for option A and B perpendicular, neither parallel nor perpendicular , parallel

Answer 1

y= -3x+2

slope A = -3

Slope B = 1/3

Perpendicular lines

1) Rewriting each equation in the slope-intercept form i.e.

y=mx+b

`\begin{gathered} y=(1)/(3)x+4 \\ 3x+y=2\Rightarrow y=-3x+2 \\ \mleft\{\begin{aligned}y=(1)/(3)x+4 \\ y=-3x+2\end{aligned}\mright. \end{gathered}`

2) The slope, as it is written in the slope-intercept form is the coefficient that comes along the x, so the slope for A is

`\begin{gathered} \text{slope for A =}(1)/(3) \\ \text{slope for B= -3} \end{gathered}`

3)We have the following rules to determine two lines position:

Parallel lines same slope

Perpendicular lines: reciprocal and opposite lines

For example -3 and 1/3