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.