Equation of a line in slope-intercept form is y = 0.2 x – 361.3.
Solution:
To find the equation for the linear function between 1934 and 1950.
Points on the line 1934 and 1950 are (1934, 1) and (1950, 4).
So, [tex]x_1=1934, x_2=1950, y_1=1, y_2=1934[/tex]
Slope of the line formula:
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]$m=\frac{4-1}{1950-1934}[/tex]
[tex]$m=\frac{3}{16}[/tex]
Let us use the point-slope formula to find the slope-intercept form.
Equation of a line in point-intercept form:
[tex]y-y_1{=m\left(x-x_{1}\right)[/tex]
Substitute [tex]x_1=1950, y_1=4[/tex] and [tex]m=\frac{3}{16}[/tex].
[tex]$y-4=\frac{3}{16} \left(x-1950\right)[/tex]
[tex]$y-4=\frac{3}{16} x-\frac{5850}{16}[/tex]
[tex]$y-4=\frac{3}{16} x-\frac{2925}{8}[/tex]
Add 4 on both sides of the equation.
[tex]$y=\frac{3}{16} x-\frac{2893}{8}[/tex]
y = 0.1875 x – 361.265
y = 0.2 x – 361.3
Equation of a line in slope-intercept form is y = 0.2 x – 361.3.
