Step-by-step explanation:
1. 9x + 3y = -18
a. Slope-intercept form: y = -3x - 6
b. Slope and y-intercept: Slope = -3, y-intercept = (0, -6)
c. Graphing: Plot the y-intercept (0, -6). Use the slope (-3/1) to go down 3 units and right 1 unit to plot another point. Connect the points to create the line.
d. Intercepts:
x-intercept: Set y = 0, solve for x: 9x = -18, x = -2. Intercept = (-2, 0)
y-intercept: Already given as (0, -6)
e. Relationship to y = x + 8: Perpendicular. Their slopes are negative reciprocals (-3 and 1).
2. y = 3x + 1
a. Standard form: -3x + y = 1
b. Slope and y-intercept: Slope = 3, y-intercept = (0, 1)
c. Graphing: Same process as in 1.c.
d. Intercepts: Same process as in 1.d.
e. Relationship to -3x + y = 7: Parallel. They have the same slope (3).
3. (4, -3) (2, 3)
a. Slope: m = (-3 - 3) / (4 - 2) = -6/2 = -3
b. Equation (slope-intercept): y - 3 = -3(x - 2), y = -3x + 9
Equation (standard form): 3x + y = 9
c. Intercepts:
x-intercept: Set y = 0, solve for x: 3x = 9, x = 3. Intercept = (3, 0)
y-intercept: Already given as (0, 9)
d. Parallel equation: y = -3x + 5 (same slope, different y-intercept)
e. Perpendicular equation: y = 1/3 x + 2 (negative reciprocal slope, different y-intercept)
4. (3, 0) (0, -12)
a. Slope: m = (0 - (-12)) / (3 - 0) = 12/3 = 4
b. Equation (slope-intercept): y - 0 = 4(x - 3), y = 4x - 12
Equation (standard form): 4x - y = 12
c. Intercepts:
x-intercept: Set y = 0, solve for x: 4x = 12, x = 3. Intercept = (3, 0)
y-intercept: Already given as (0, -12)
Graphing for 3 and 4: Plot the intercepts and connect the points to create the lines.
