Math Coursework: Write the Point-Slope Form of the Equation

Math
Name
Institution
#21 Write the point-slope form of the equation of the line described.
through: (5, 1), parallel to y =1/5x + 1
y=mx+b
Parallel lines have the same slope
Therefore, the slope m for the line described by (5, 1) = 1/5
Point-slope form of the equation is given by y – y1 = m(x – x1)
(x1 , y1) = point on the line = (5, 1)
Answer: y – 1= 1/5(x – 5)
#22 Write the slope-intercept form of the equation of the line described.
through: (-4, -5), perpendicular to y = -2/5x + 4
y=mx+b
The slope m for the perpendicular line described by (-4, -5) = 5/2
y – y1 = m(x – x1)
(x1 , y1) = point on the line = (-4, -5)
y + 5 = 5/2(x+4)
y=5/2x +5
Answer: y=5/2x +5
#24 Solve the system of equations by the method of elimination.
5x + 4 y = 23
-x - 12 y = 29
To eliminate y, first multiply the first equation by 3
3(5x + 4 y = 23)
-x - 12 y = 29
Then add the second equation to the first equation
15x +12y = 69
-x - 12 y = ...