A pool had a little bit of water in it and the owners decided it was time to fill it up. There is a linear relationship between the amount of time the pol had been filling and the amount of water in the pool. After 100 minutes of filling there were 3000 gallons in the pool. After 240 minutes of filling there were 5520 gallons in the pool. Write an equation that models the linear relationship described above. DO NOT USE ANY SPACES between variables, constants, equals signs, and operation signs. For example, DO NOT enter \( y=2 x+1 \). DO ENTER: \( y=2 x+1 \). Put parentheses around constants that are fractions like this: \( y=(2 / 3) x-(1 / 2) \) To write your equation, use the variables: \( m= \) the amount of time the pool had been filling (minutes) \( g= \) the number gallons in the pool The equation in slope-intercept form is
Solución de inteligencia artificial de Upstudy
Responder
Solución
¡Inicia sesión para desbloquear respuestas gratis!
Una plataforma de aprendizaje en la que confían millones de estudiantes y profesores reales.
Descubrir Respondido por UpStudy AI y revisado por un tutor profesional
The Deep Dive
To find the slope of the line, we use the two points given: (100, 3000) and (240, 5520). The slope \( (m) \) can be calculated as follows: \( m=\frac{g_2-g_1}{m_2-m_1}=\frac{5520-3000}{240-100}=\frac{2520}{140}=18 \) Now we can write the equation in point-slope form: \( g - 3000 = 18(m - 100) \) To convert to slope-intercept form: \( g = 18m - 1800 + 3000 \) This simplifies to: \( g = 18m + 1200 \) So the final equation is: \( g = 18m + 1200 \) Putting it in the required format, the equation in slope-intercept form is: \( g=18m+1200 \)
