What is the equation of the line perpendicular to 7x − 2y = −24 that contains the point (14, −2)?

A y = -2/7x

B y = -2/7x + 2

C y = -7/2x + 12

D y = 7/2x - 6

hay24
Apr 22, 2018

#3**+1 **

I generally find it to be easier when the equations are put in slope-intercept form (or y=mx+b). In order to convert the original equation to this form, solve for y. The slope-intercept form tells one important information about a certain equation.

- m = slope of line
- b = y-intercept

\(7x-2y=-24\) | To solve for y, it is probably easiest to subtract 7x from both sides. |

\(-2y=-7x-24\) | Finally, divide by -2. |

\(y=\textcolor{red}{\frac{7}{2}}x+\textcolor{blue}{12}\\ \textcolor{red}{m}=\textcolor{red}{\frac{7}{2}}\\ \textcolor{blue}{b}=\textcolor{blue}{12} \) | |

One special property about perpendicular lines is that their slopes are opposite reciprocals from each other. Since we know the slope of the given line, we can figure out the slope of the perpendicular one.

\(\frac{7}{2}\Rightarrow{-\frac{7}{2}}\Rightarrow-\frac{2}{7}\)

-2/7 is the slope of the perpendicular line. However, we know another requirement about this line: It passes through the coordinate (14,-2). Let's take this information into account. We know that the equation, thus far, is \(y=-\frac{2}{7}x+b\).

\(y=-\frac{2}{7}x+b\) | b is the only variable remaining in this equation. We know that, based on the previous info, that when x=14, y=-2. This was preset by the given coordinate. Let's plug those values in and solve for the missing variable: b. |

\(-2=-\frac{2}{7}*14+b\) | 14 and 7 are common factors, so this will divide evenly. |

\(-2=-4+b\) | Add 4 to both sides to isolate b. |

\(2=b\) | Now, let's write the final equation in slope-intercept form (because that is the form that the answer choices are given in). |

\(y=-\frac{2}{7}x+2\), which is B in the answer choices provided.

TheXSquaredFactor
Apr 22, 2018

#3**+1 **

Best Answer

I generally find it to be easier when the equations are put in slope-intercept form (or y=mx+b). In order to convert the original equation to this form, solve for y. The slope-intercept form tells one important information about a certain equation.

- m = slope of line
- b = y-intercept

\(7x-2y=-24\) | To solve for y, it is probably easiest to subtract 7x from both sides. |

\(-2y=-7x-24\) | Finally, divide by -2. |

\(y=\textcolor{red}{\frac{7}{2}}x+\textcolor{blue}{12}\\ \textcolor{red}{m}=\textcolor{red}{\frac{7}{2}}\\ \textcolor{blue}{b}=\textcolor{blue}{12} \) | |

One special property about perpendicular lines is that their slopes are opposite reciprocals from each other. Since we know the slope of the given line, we can figure out the slope of the perpendicular one.

\(\frac{7}{2}\Rightarrow{-\frac{7}{2}}\Rightarrow-\frac{2}{7}\)

-2/7 is the slope of the perpendicular line. However, we know another requirement about this line: It passes through the coordinate (14,-2). Let's take this information into account. We know that the equation, thus far, is \(y=-\frac{2}{7}x+b\).

\(y=-\frac{2}{7}x+b\) | b is the only variable remaining in this equation. We know that, based on the previous info, that when x=14, y=-2. This was preset by the given coordinate. Let's plug those values in and solve for the missing variable: b. |

\(-2=-\frac{2}{7}*14+b\) | 14 and 7 are common factors, so this will divide evenly. |

\(-2=-4+b\) | Add 4 to both sides to isolate b. |

\(2=b\) | Now, let's write the final equation in slope-intercept form (because that is the form that the answer choices are given in). |

\(y=-\frac{2}{7}x+2\), which is B in the answer choices provided.

TheXSquaredFactor
Apr 22, 2018