The line passing through (4,3) and (y,0) is parallel to the line passing through (−1,−2) and (3,0). Find y.

Since the two lines are parallel, their slopes must be equal (m
1
​
=m
2
​
).

The formula for the slope of a line passing through (x
1
​
,y
1
​
) and (x
2
​
,y
2
​
) is:

m=
x
2
​
−x
1
​

y
2
​
−y
1
​

​

Let m
1
​
be the slope of the line passing through (4,3) and (y,0):

m
1
​
=
y−4
0−3
​
=
y−4
−3
​

Let m
2
​
be the slope of the line passing through (−1,−2) and (3,0):

m
2
​
=
3−(−1)
0−(−2)
​
=
4
2
​
=
2
1
​

Equating the two slopes (m
1
​
=m
2
​
):

y−4
−3
​
=
2
1
​

Cross-multiplying yields:

−6=y−4
y=−6+4
y=−2