Answer:
1) 

2) 

3)

Step-by-step explanation:
We want to write the equation of the line that passes through the points (7, -4) and (-1, 3) first in point-slope form and then in slope-intercept form. 
1)
First and foremost, we will need to find the slope of the line. So, we can use the slope-formula: 

Let (7, -4) be (x₁, y₁) and let (-1, 3) be (x₂, y₂). Substitute them into our slope formula. This yields: 

Subtract. So, our slope is: 

2) 
Now, let's use the point-slope form: 

We will substitute -7/8 for our slope m. We will also use the point (7, -4) and this will be our (x₁, y₁). So, substituting these values yield: 

Simplify. So, our point-slope equation is: 

3) 
Finally, we want to convert this into slope-intercept form. So, let's solve for our y. 
On the right, distribute: 

Subtract 4 from both sides. Note that we can write 4 using a common denominator of 8, so 4 is 32/8. This yields: 

Subtract. So, our slope-intercept equation is: 

And we're done!