Question

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Answer 1

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 $\frac{y_{2}- y_{1} }{x_{2}- x_{1} }$.  In this problem, y2=2, y1=7, x2=1, and x1=-4.  Plug those values into the slope formula to find the slope.

$\frac{2-7}{1--4}= \frac{-5}{5} =-1$

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!