Algebra2 Part 11a Chapter 1

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In trying to figure out at what rate a swimming pool fills up there is a slope and a rate from 18 inches to 32 inches. Solution a sketch can be used to help but it is optional. Again, there are the two opposite lines y and x. A line drawn marked with a dot at (1,18 and another point at the other end of (5, 32); Asking for the rate of change of a line is the same as asking for its 'slope'. Rate of change = m = 32-18/5-1= 14 inches/4 hours = 3.5 inches per hour "Note that for rate of change, we usually include units, in this case, inches per hour. The water level in the pool is increasing 3.5 inches each hour. The next section is 'Equations of Lines' "The equation Ax + By = C is often called the 'general form' of the equation of a line. Some people prefer Ax + By + C= 0." " It is called the general form because any line, whether horizontal, vertical, or diagonal, can be written in this form. Unfortunately, the A, B, and C by themselves don't really stand for anything. For lines where B is not = 0, in other words, for lines that are not vertical, two other forms of equations of a line are very useful both graphing lines and for modeling with lines." "Slope-Intercept Equation' of a line From Algebra 1 you may remember, any nonvertical line can be written in 'slope-intercept form'. y = mx + b where m is the slope, b is the y-intercept Example 1.17 Write the equation of the line 3x + 5y = 20 in 'slope-intercept form' and then graph the line. Solution Writing the equation in 'slope-intercept form ' means you must solve for y 3x + 5y = 20 5y = -3x + 20 Subtract to move x to the right side. Write the term with x to the left of the constant (not at the end). 5y/5= -3x/5 + 20/5 Divide each term by the coefficient of y. Write separately to avoid mistakes. y = - 3/5 of x +4 Simplify "From this, we see that the slope is -3/5 and the 'y-intercept' is 4. This is easy to graph because the slope goes down 3 and across 5 and where the y line that goes through the x line the line starts right of the count 4 up. By repeating the 'slope ' and marking with a dot each time you can draw the line connecting them. Common errors: "Be sure to plot 4 on the y-axis. not on the -axis. When dividing by the coefficient of y, divide each term separately. Some students write 5y/5 = (-3x + 20) divided by 5 but then simplify incorrectly to y = -3x/5 +20 or y = -3x + 4. (Continue)