Complete Question:
The growth of baby girl Claire is displayed in the graph below. (4, 22) (14, 30)
Answer:
Point Slope: [tex]y - 22 = 0.8(x - 4)[/tex]
Slope Intercept: [tex]y = 0.8x +18.8[/tex]
y intercept: [tex]b = 18.8[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (4,22)[/tex]
[tex](x_2,y_2) = (14,30)[/tex]
Solving (a) Point slope
Using point slope form, an equation is of the form
[tex](y_2 - y_1) = m(x_2 - x_1)[/tex]
First, we need to solve for slope (m):
Make m the subject
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Substitute values for x and y
[tex]m = \frac{30 - 22}{14 - 4}[/tex]
[tex]m = \frac{8}{10}[/tex]
[tex]m = 0.8[/tex]
Next, we form a linear relationship
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex]m = 0.8[/tex] and [tex](x_1,y_1) = (4,22)[/tex]
[tex]y - 22 = 0.8(x - 4)[/tex]
Solving (b): Slope Intercept
[tex]y - 22 = 0.8(x - 4)[/tex]
Open Bracket
[tex]y - 22 = 0.8x - 3.2[/tex]
Add 22 to both sides
[tex]y - 22 +22= 0.8x - 3.2 + 22[/tex]
[tex]y = 0.8x +18.8[/tex]
Solving (c): The y intercept
The general form of an equation is:
[tex]y = mx + b[/tex]
Where b represents the y intercept
By comparison with [tex]y = 0.8x +18.8[/tex]
[tex]b = 18.8[/tex]
