Final answer:
To solve the equation Y - 5 = 15(x + 3) in point-slope form, distribute the 15, add 5 to both sides to isolate Y, resulting in Y = 15x + 50. This gives us a slope of 15 and passes through the point (-3, 5).
Step-by-step explanation:
The student's question asks to solve the equation Y - 5 = 15(x + 3) in point-slope form. To solve this equation, first simplify the right side by distributing the 15 into the parentheses, resulting in Y - 5 = 15x + 45. Next, solve for Y by adding 5 to both sides of the equation, which gives us Y = 15x + 50. This equation is already in point-slope form where the slope (m) is 15, and the point (x, y) through which the line passes is (-3, 5).
Considering the additional context provided, the line Y2 = -173.5 + 4.83x - 2(16.4), and line Y3 = -173.5 + 4.83x + 2(16.4) have the same slope as the line of best fit which is 4.83. These lines illustrate how the slope affects the position of parallel lines as they share the same slope but differ in their y-intercepts due to the constant term differences.
To solve the equation Y - 5 = 15(x - (-3)) in point-slope form, we need to isolate the y-term and rewrite the equation in the form y = mx + b, where m represents the slope and b represents the y-intercept.
First, simplify the equation: Y - 5 = 15(x + 3).
Next, distribute 15 to both terms inside the parentheses: Y - 5 = 15x + 45.
Then, move the constant term to the other side of the equation: Y = 15x + 50.
Therefore, the equation Y - 5 = 15(x - (-3)) in point-slope form is Y = 15x + 50.