Linear Mathematics Review 1
1. The straight line goes through the points (-3, 2) and
(4, -1). Find the slope of the line .
According to the formula we have
2. Write a point-slope equation for the line from Problem
If we know the slope m and a point on the straight line we can write an equation in the point-slope form as. If we use e.g. the point (-3,2) then we can write
3. Write the slope- intercept equation for the line from
We will solve the equation we got in the previous problem for y.
4. Write an equation of the line parallel to the line from
Problem 1 and going through the
Parallel lines have equal slopes and therefore we can write an equation of this parallel line in the point-slope form
Solving for y we get an equation in the slope- intercept form
5. Write an equation of the line perpendicular to the line
from Problem 1 and going
through the point (1,3).
The slopes of perpendicular lines are negative reciprocals and therefore the slope of the perpendicular line is 7/3 and its equation in the point-slope form Solving for y we get an equation in the slope-intercept form
6. Graph the lines from Problems 1 and 5 in the same coordinate system.
7. Find the point of intersection of the lines from
Problems 1 and 5.
We have to solve the system of equations
Because the left parts are equal so are the right parts.
Multiplying both parts
by the common denominator , 21, we get
After we plug this value of x into the firs equation we get
8. The straight line has the x-intercept -2 and the
y-intercept 3. Write an equation of the
line. We use the formula where a and b are the x-intercept and the y-intercept, respectively. In our case
9. If the price of a CD-player is $40 the demand is 4000.
If the price of the same
CD- player is $60 the demand is 3000. Assuming that the demand is a linear function
of the price find the demand if the price is $55.
First we need the slope-intercept equation of the line through the points (40, 4000) and (60, 3000). The slope of the line is Using for example the first point we can write an equation of the line in the point-slope
form . From here, If then.
10. A small company produces dolls. The permanent monthly
expenses are $6000 and the
Cost of producing a doll is $3. If the dolls sell for $10 each what is the breakeven
The cost of producing x dolls is The corresponding revenue is To find the break-even point we have to solve the equation or We have