Question

• Write an equation of the line, and

• sketch a graph of the line including the given point(s).
1. The line with slope -6 and through the point (-14, 14).
2. The line through the points (-9,0) and (-4,4).

Answer 1

↓↓↓

Explanation:

1. It's given that the slope is -6 and the line passes through the point (-14,14). So we can solve for the equation of the line, let's solve for it. Using the given slope and point, it would look like:

-6(-14) = 14
84 = 14

Now, obviously, 84 doesn't equal 14. This is just so we can figure out the y-intercept. Now, what would we need to subtract from 84 to get 14?

84 - 70 = 14

Now, plug it into the original equation.

-6(-14) - 70 = 14
84 - 70 = 14

Now we can say that the equation for the line is -6x - 70.

2. For this line, we aren't given a slope or y-intercept, only 2 points. Those 2 points are (-9,0) and (-4,4). But with these 2 points, we can figure out the slope, which we can then figure out the y-intercept.

If you don't know, slope is how many times y moves up or down divided by how many times x moves. Looking at the 2 points, we can see that going over 5 units makes the line go up 4 units. That would be
`(4)/(5)`. Slope would be negative if we were going down 4 units, but since we're not, it's positive.

Now, like #1, let's use the slope and points to make an equation.

`(4)/(5)`(-4) = 4

`(-16)/(5)` = 4

Again,
`(-16)/(5)` doesn't equal 0. So what do we need to add to
`(-16)/(5)` to make it 4?

`(-16)/(5)` +
`\frac{36} {5}` = 4

`(20)/(5)` = 4

Now, we think that the y-intercept is
`\frac{36} {5}`. To double check, we'll use the other point given.

`(4)/(5)`(-9) +
`\frac{36} {5}` = 0

`(-36)/(5)` +
`\frac{36} {5}` = 0

Now, we can say that the equation for the line is
`(4)/(5)`x +
`\frac{36} {5}`. Another way we can write that is 0.8x + 7.2.