(a) The slope of the line is approximately -0.926.
(b) The equation of the line in point-slope form is y - 140 = -0.926(x - 150).
(c) The equation of the line in slope-intercept form is y = -0.926x - 1.1.
(d) The equation of the line in standard form is 92.6x + 100y = -110.
a) To find the slope of the line, we need to determine the change in the number of children's tickets sold (y) divided by the change in the number of adult tickets sold (x). Let's select two points on the line:
Point 1: (x1, y1) = (150, 140)
Point 2: (x2, y2) = (204, 90)
Using the slope formula (m = (y2 - y1) / (x2 - x1)), we can calculate the slope:
m = (90 - 140) / (204 - 150)
m = -50 / 54
m ≈ -0.926
Therefore, the slope of the line is approximately -0.926.
(b) To find the equation of the line in point-slope form, we can use one of the points on the line and the slope we just calculated. Let's use Point 1:
y - y1 = m(x - x1)
y - 140 = -0.926(x - 150)
This is the equation of the line in point-slope form.
(c) To convert the equation to slope-intercept form (y = mx + b), we need to solve for y:
y - 140 = -0.926x + 138.9
y = -0.926x - 1.1
Therefore, the equation of the line in slope-intercept form is y = -0.926x - 1.1.
(d) To convert the equation to standard form (Ax + By = C), we need to eliminate the decimals by multiplying both sides of the equation by 100:
100y = -92.6x - 110
Next, we can move all the terms to one side to get the equation in the standard form:
92.6x + 100y = -110
Therefore, the equation of the line in standard form is 92.6x + 100y = -110.