Using point-slope form, write the equation of the line that describes this scenario. Then, rewrite the equation in slope-intercept form.
In order to enter the state fair, there is an admission cost. Each game is $3. Steven went to the state fair, played 4 games and spent a total of $20 on admission and games.
Point-Slope Form Equation:
Slope-Intercept Form Equation:
Point-Slope Form Equation: y - y1 = m(x - x1)
Let x represent the number of games played and y represent the total cost.
We are given the point (4, 20), where x1 = 4 and y1 = 20. We can also determine the slope (m) by dividing the change in y by the change in x. In this case, since each game costs $3, for each additional game the cost increases by $3.
Therefore, m = 3.
Plugging in these values, the equation becomes:
y - 20 = 3(x - 4)
Slope-Intercept Form Equation: y = mx + b
To rewrite the equation in slope-intercept form, we need to solve for y.
Expanding the point-slope equation:
y - 20 = 3x - 12
y = 3x - 12 + 20
y = 3x + 8