1. Use an x/y table and graph the equation, identifying the y intercept.
y = 2x – 5
y intercept when x = 0
y = -5 is the y intercept
x = -2, y = -9
x = -1, y = -7
x = 0, y = -5
x = 1, y = -3
x = 2, y = -1
2. Find the intercepts of the equation. Use an x/y table and graph the equation.
x – 2y = 6
x intercept: set y to 0: x = 6
y intercept: set x to 0: y = -3
-2y = 6 – x
y = (1/2)x – 3
x = -2, y = -4
x = -1, y = -3.5
x = 0, y = -3
x = 1, y = -2.5
x = 2, y = -2
5. Graph the line containing the given pairs of points and find the slope.
(-5,-2) ; (5,4)
slope = rise/run
= (4-(2))/(5-(-5))
= 6/10
= 3/5
Graph:
6. At one point, Beartooth Highway in Yellowstone National Park rises 315ft over a horizontal distance of 4500ft. Find the slope, or grade, of the road. Be sure to graph.
Slope = rise/run
= 315/4500
= 0.07
7. Find the slope, if it exists.
y = - 5/8 x – 3
y = mx + b, m is the slope
slope = -5/8
8. Find the slope and the y- intercept.
y = -9x + 46
y = mx + b, m is the slope, b is the y intercept:
slope = -9
y intercept = 46
9. Find the equation of the line with the given slope and y- intercept.
Slope = -2.8; y- intercept (0,19)
Y = mx+b
Y = -2.8x + 19
10. Find an equation of the line containing the given point and with the slope.
(1, 2), m = 3
Point slope form:
y-y1 = m(x-x1)
y-2 = 3(x-1)
y-2 = 3x – 3
y = 3x - 1
11. Find an equation of the line containing the given pair of points.
(5, 7) and (-1, 1)
slope = rise/run
= (1-7)/(-1-5)
= -6/-6
= 1
Point slope form:
y-y1 = m(x-x1)
y-7 = (x-5)
y = x + 2
12. Compose a line graph illustrating the percent of the female population age 16 and older in the work force for years since 1950. Use y as the percentage of female population in the labor force on the graph. Use x as the year (beginning in 1950) on the graph.
a) Find an equation of the line (0, 33.9) and (53, 59.5)
slope = rise/run
= (59.5-33.9)/(53-0)
= 0.483
y = 0.483x + 33.9
b) What is the rate of change in the percent of female workers in the labor force with respect to time?
0.483% per year (that’s the slope)
c) Use the equation to find the percent of female workers in the labor force in 2005.
Plug in 55:
0.483*55 + 33.9
= 60.465%
Graph:
13. Solve the system by graphing.
x + y = 4, x – y = 8
Solve each for y:
Y = 4 – x
-y = 8 – x
y = x – 8
Graph:
Solution: x = 6, y = -2