# Determine if the line passes through the points (0,2) and ( -1, 3) is parallel to the line (7/2)y + (7/4)x + 35/2 = 0

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We have a line passes through the point ( -1,3) and (0,2)

Also we have the line (7/2)y + (7/4) x + 35/2 = 0

To determine if both lines are parallel we need to write using the slope form for both lines.

If both slopes are equal , then the lines are parallel.

Let us determine the line passes through the given points:

(y-y1) = m(x-x1)

y- 2 = m (x-0)

m = (y2-y1)/(x2-x1)

= (2-3)/ (0--1)

= -1/1 = -1

==> y-2 = -1(x)

**==> y= -x + 2 ==> the slope m1 = -1**

** **

Now let us rewrtie the equation for thwe line:

( (7/2)y + (7/4) x + 35/2 = 0

Let us multiply by 2/7

==> y + (1/2)x + 5 = 0

==> y= -(1/2)x - 5

Then the slope m2 = -1/2

**Then m1 and m2 are different**

**Then, we conclude that both line are NOT parallel.**

The equation of the line passing through the points (0,2) and (-1,3) is y=-1x+2.

Putting the equation (7/2)y + (7/4)x + 35/2 = 0 in standard form:

y = -1/2 x + 5

Since the slopes of these two lines are not equal, they are not parallel. In fact they intersect near the point (14,-12)