To solve either part of this problem, you first need to find the slope of the line. You can do this using the slope formula [tex]\frac{y_{2}- y_{1} }{x_{2}- x_{1} }[/tex]. In this problem, y2=2, y1=7, x2=1, and x1=-4. Plug those values into the slope formula to find the slope.
[tex]\frac{2-7}{1--4}= \frac{-5}{5} =-1[/tex]
The slope of the line is -1.
For the first part of the question, you need to create the point-slope equation. Point-slope equations follow the model (y-y)=m(x-x), where m is the slope and x and y are coordinates.
We know the slope is -1. To find the coordinates, take x and y from one of the ordered pairs (it doesn't matter which, but you cannot take x from the first one and y from the second). We'll use the first one: (-4, 7).
The point-slope equation is (y-7)=-1(x+4).
The x is "plus" because the coordinate is negative, and subtracting a negative number is the same as addition.
To find the slope-intercept form, you can use the point-slope equation and solve for y. Start by distributing the -1. The equation becomes:
y-7=-x-4
Next, add 7 to both sides. It becomes:
y=-x+3
Slope-intercept form follows the model, y=mx+b, where m is the slope and b is the intercept. y=-x+3 matches this model because -1 is the slope and 3 is the intercept.
The slope-intercept equation is y=-x+3.
Hope this helps and makes sense!
