Find the equation of the line through the points \( (-3,-4) \) and \( (1,-5) \). Write your answer in the slope-intercept form \( y=m x+b \). \( y=\square \)
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.

Respondido por UpStudy AI y revisado por un tutor profesional
The Deep Dive
To find the equation of the line through points \( (-3,-4) \) and \( (1,-5) \), we first calculate the slope \( m \). The slope formula is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - (-4)}{1 - (-3)} = \frac{-5 + 4}{1 + 3} = \frac{-1}{4} \] Now that we have the slope \( m = -\frac{1}{4} \), we use the slope-intercept form \( y = mx + b \). We can use one of the points to find \( b \). Let's use the point \( (-3, -4) \): \[ -4 = -\frac{1}{4}(-3) + b \] \[ -4 = \frac{3}{4} + b \implies b = -4 - \frac{3}{4} = -\frac{16}{4} - \frac{3}{4} = -\frac{19}{4} \] So, the equation of the line is: \[ y = -\frac{1}{4}x - \frac{19}{4} \] Thus, filling in the blank: \( y = -\frac{1}{4}x - \frac{19}{4} \)
