How do you tell whether the lines for each pair of equations are parallel, perpendicular, or neither: y=-4x+3, -2x+8y=5?

May 3, 2018

Answer:

$\text{lines are perpendicular}$

Explanation:

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$\text{express both equations in this form and consider their}$
$\text{slopes}$

• " parallel lines have equal slopes"

• " the product of the slopes of perpendicular lines equals -1"

$y = - 4 x + 3 \leftarrow \textcolor{b l u e}{\text{is in slope-intercept form}}$

$\text{with slope m } = - 4$

$\text{rearranging "-2x+8y=5larrcolor(blue)"add 2x to both sides}$

$\Rightarrow 8 y = 2 x + 5$

$\text{divide all terms by 8}$

$\Rightarrow y = \frac{1}{4} x + \frac{5}{8} \leftarrow \textcolor{b l u e}{\text{in slope-intercept form}}$

$\text{with slope } = \frac{1}{4}$

$- 4 \ne \frac{1}{4} \text{ hence lines are not parallel}$

$- 4 \times \frac{1}{4} = - 1 \text{ hence lines are perpendicular}$