To find the equation of the line that passes through (-4,3) and (-3,1) in slope-intercept form, we can use the following steps:
1. Find the slope of the line.
2. Substitute the slope and one of the points into the slope-intercept form equation, and solve for the y-intercept.
3. Write the equation in slope-intercept form.
**Finding the slope**
The slope of a line is calculated using the following formula:
```
m = (y2 - y1) / (x2 - x1)
```
where $(x1, y1)$ and $(x2, y2)$ are any two points on the line.
In this case, our two points are (-4,3) and (-3,1). Substituting these values into the slope formula, we get:
```
m = (1 - 3) / (-3 - (-4)) = -2 / 1 = -2
```
Therefore, the slope of the line is -2.
**Finding the y-intercept**
The slope-intercept form of a line equation is:
```
y = mx + b
```
where m is the slope of the line and b is the y-intercept.
We know that the slope of the line is -2, so we can substitute that into the slope-intercept form equation. We can also substitute one of the points on the line, such as (-4,3). This gives us the following equation:
```
3 = -2 * (-4) + b
```
```
3 = 8 + b
```
```
b = 3 - 8
```
```
b = -5
```
Therefore, the y-intercept of the line is -5.
**Writing the equation in slope-intercept form**
Now that we know the slope and y-intercept of the line, we can write the equation in slope-intercept form:
```
y = mx + b
```
```
y = -2x - 5
```
Therefore, the equation of the line that passes through (-4,3) and (-3,1) in slope-intercept form is **y = -2x - 5**.