Question

The graph shows the total number of goals scored by the US during several FIFA World Soccer tournaments. Find the equation for the linear function between 1934 and 1950. Write the equation in slope-intercept form. Round the slope and intercept to the nearest tenth

Answer 1

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,
`x_1=1934, x_2=1950, y_1=1, y_2=1934`

Slope of the line formula:

`$m=(y_(2)-y_(1))/(x_(2)-x_(1))`

`$m=(4-1)/(1950-1934)`

`$m=(3)/(16)`

Let us use the point-slope formula to find the slope-intercept form.

Equation of a line in point-intercept form:

`y-y_1{=m\left(x-x_(1)\right)`

Substitute
`x_1=1950, y_1=4` and
`m=(3)/(16)`.

`$y-4=(3)/(16) \left(x-1950\right)`

`$y-4=(3)/(16) x-(5850)/(16)`

`$y-4=(3)/(16) x-(2925)/(8)`

Add 4 on both sides of the equation.

`$y=(3)/(16) x-(2893)/(8)`

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.