#1**+2 **

To find the equation that passes through \((-4,0)\) and is parallel to the line \(y=\frac{3}{4}x-2\), we must understand a few properties.

1) Parallel lines have the same slope.

This fact, alone, can help us do half the problem. The slope of the line \(y=\frac{3}{4}x-2\) is \(\frac{3}{4}\). As I stated above, parallel lines have the same slope, so the equation of this unknown line is \(\frac{3}{4}\).

We have deduced already that this unknown line is in the form of \(y=\frac{3}{4}x+b \). The only thing to find now is the b:

\(y=\frac{3}{4}x+b \) | Now, plug in a coordinate that we know is on the line. In this case, we only know that \((-4,0)\) lies on the line. Plug it in for x and y. |

\(0=\frac{3}{4}*\frac{-4}{1}+b\) | Simplif the right hand side. |

\(0=-3+b\) | Add 3 to both sides of the equation. |

\(b=3\) | |

We have found both of the mystery values to construct the proper equation of a line. It is \(y=\frac{3}{4}x+3\)

TheXSquaredFactor
Sep 21, 2017

#1**+2 **

Best Answer

To find the equation that passes through \((-4,0)\) and is parallel to the line \(y=\frac{3}{4}x-2\), we must understand a few properties.

1) Parallel lines have the same slope.

This fact, alone, can help us do half the problem. The slope of the line \(y=\frac{3}{4}x-2\) is \(\frac{3}{4}\). As I stated above, parallel lines have the same slope, so the equation of this unknown line is \(\frac{3}{4}\).

We have deduced already that this unknown line is in the form of \(y=\frac{3}{4}x+b \). The only thing to find now is the b:

\(y=\frac{3}{4}x+b \) | Now, plug in a coordinate that we know is on the line. In this case, we only know that \((-4,0)\) lies on the line. Plug it in for x and y. |

\(0=\frac{3}{4}*\frac{-4}{1}+b\) | Simplif the right hand side. |

\(0=-3+b\) | Add 3 to both sides of the equation. |

\(b=3\) | |

We have found both of the mystery values to construct the proper equation of a line. It is \(y=\frac{3}{4}x+3\)

TheXSquaredFactor
Sep 21, 2017