**1. Which of the following lines is parallel with the graph of the given equation AND goes through the given point below?**

**y = 8x + 5**

Point (1,9)

The answer would be C because parallel lines must have the same slope and the slope needs to be 8. C fits that description but so does everything else, so we need to figure out the y-intercept. Because the slope is 8, or **8/1**, for every 1 change in x, there will be **8 changes in y.** So, because (1,9) is the point given, we can subtract one from the x and we'll have to subtract 8 from the y. Therefore, our new point will be **(0,1)** which means our y-intercept is **1.** C is the only answer choice that fits this.

**2. Which of the following lines is perpendicular with the graph of the given equation AND goes through the given point below?**

**-3x + 2y - 5 = 7**

Point (-3,4)

First, let us put this into slope-intercept form. That will give us:

**-3x + 2y - 5 = 7**

*(Add 5 to both sides)*

**-3x + 2y = 12**

*(Add 3x to both sides)*

**2y = 3x + 12**

*(Divide both sides by 2)*

**y = 3/2x + 6**

Therefore, our slope is **3/2** and our y-intercept is **6. **Now, because we want to find a line perpendicular to this line, we must find the **negative reciprocal **of the slope, or **-2/3**. This will be the slop we want. Now, **choices B and C fit the description,** so we need to find the y-intercept of our new line. We have the point (-3,4) so, because our slope is **-2/3**, we can add three to the x axis and subtract 2 from the y. So, our new y-intercept is **(0,2).** Therefore, we need a **+2** at the end of our new equation for the line. So the answer would be B.

**Answer key:**

**1) C**

**2) B**