Slippery Slopes

Learning Focus

Use slope to decide whether lines are parallel or perpendicular and to write equations of such lines.

Big idea

Slope is $m=\frac{y_2-y_1}{x_2-x_1}$.

• Parallel lines have equal slopes.
• Perpendicular lines have slopes that are negative reciprocals: $m_1m_2=-1$.
• Use point-slope or slope-intercept form to write the new line.

Worked example

Slope through $(1,2),(5,10)$: $\frac{8}{4}=2$.

A line parallel to $y=-3x+4$ has slope $-3$.

A line perpendicular to $y=2x+1$ has slope $-\frac12$; through $(0,5)$ it is $y=-\frac12x+5$.

Takeaways

• Parallel: same slope.
• Perpendicular: negative reciprocal.
• Use a point to find the intercept.