MTH
030 -- Elementary Algebra -- Exercise Solutions
Section:
3.6
17.
Write the equation of the line that passes through the point (2,
1) with slope 3 .
Solution: The point slope form of the equation of a line is y
- y1 = m(x - x1) where
the coordinates of the known point are
(x1, y1) and
m is the known slope.
In
this problem we have y - 1 = 3(x - 2) = 3x - 6. The equation
is y - 1 = 3x - 6
Add 1 to
both sides of the equation to obtain the more desirable slope intercept form
of the equation of this line
y = 3x - 5.
18.
Write the equation of the line that passes through the point (4,
3) with slope 2 .
Solution: The point slope form of the equation of a line is y
- y1 = m(x - x1) where
the coordinates of the known point are (x1, y1) and m
is the known slope.
In
this problem we have y - 3 = 2(x - 4) = 2x - 8. The
equation is y - 1 = 3x - 6
Add 3 to
both sides of the equation to obtain the more desirable slope intercept form
of the equation of this line
y = 3x - 5.
19.
Write the equation of the line that passes through the point (-5,
-1) with slope -(4/5).
Solution: The point slope form of the equation of a line is y
- y1 = m(x - x1) where
the coordinates of the known point are (x1, y1) and m
is the known slope.
In
this problem we have y - (-1) = -(4/5)[x - (-5)].
Performing the indicated operations yields y + 1 = -(4/5)(x
+ 5) = -(4/5)x - 4. The equation is y + 1 = -(4/5)x - 4
Add -1 to
both sides of the equation to obtain the more desirable slope intercept form
of the equation of this line
y
= -(4/5)x - 5.
20.
Write the equation of the line that passes through the point (-2,
-9) with slope -(7/8).
Solution: The point slope form of the equation of a line is y
- y1 = m(x - x1) where
the coordinates of the known point are (x1, y1) and m
is the known slope.
In
this problem we have y - (-9) = -(7/8)[x - (-2)].
Performing the indicated operations yields y + 9 = -(7/8)(x
+ 2) = -(7/8)x - 7/4. The equation is y + 9 = -(7/8)x - 7/4
Add -9 to
both sides of the equation to obtain the more desirable slope intercept form
of the equation of this line
y
= -(7/8)x - 43/4.