Question

write the slope-intercept form of the equation of each line given the slope and y-intercept.

1. slope = -9, y-intercept = -4
2. slope = $\frac{3}{2}$, y-intercept = -4

write the slope-intercept form of the equation of each line.
3)
4)

write the slope-intercept form of the equation of the line through the given point with the given slope.

1. through: (2, 1), slope = 1
2. through: (-5, -1), slope = -4

write the slope-intercept form of the equation of the line through the given points.

1. through: (-2, 2) and (-4, 1)
2. through: (-3, -1) and (-5, 1)

Explanation:

Step1: Usar la forma pendiente-intercepto

La forma es $y = mx + b$, donde $m$ es la pendiente y $b$ es la intersección con el eje $y$.

Pregunta 1:

Sustituir $m=-9$, $b=-4$
$y = -9x + (-4)$
Simplificar: $y = -9x - 4$

Pregunta 2:

Sustituir $m=\frac{3}{2}$, $b=-4$
$y = \frac{3}{2}x + (-4)$
Simplificar: $y = \frac{3}{2}x - 4$

Step2: Calcular pendiente e intersección (Preg3)

De la gráfica, intersección $b=-2$. Tomar puntos $(0,-2)$ y $(-2,0)$
Calcular pendiente: $m=\frac{0 - (-2)}{-2 - 0}=\frac{2}{-2}=-1$
Sustituir en $y=mx+b$: $y = -1x - 2$ → $y = -x - 2$

Step3: Calcular pendiente e intersección (Preg4)

De la gráfica, intersección $b=4$. Tomar puntos $(0,4)$ y $(-3,-2)$
Calcular pendiente: $m=\frac{-2 - 4}{-3 - 0}=\frac{-6}{-3}=2$
Sustituir en $y=mx+b$: $y = 2x + 4$

Step4: Usar punto-pendiente (Preg5)

Fórmula punto-pendiente: $y - y_1 = m(x - x_1)$
Sustituir $(x_1,y_1)=(2,1)$, $m=1$
$y - 1 = 1(x - 2)$
Despejar $y$: $y = x - 2 + 1$ → $y = x - 1$

Step5: Usar punto-pendiente (Preg6)

Sustituir $(x_1,y_1)=(-5,-1)$, $m=-4$
$y - (-1) = -4(x - (-5))$
Simplificar: $y + 1 = -4(x + 5)$
Despejar $y$: $y = -4x - 20 - 1$ → $y = -4x - 21$

Step6: Calcular pendiente y b (Preg7)

Puntos $(-2,2)$ y $(-4,1)$
Calcular pendiente: $m=\frac{1 - 2}{-4 - (-2)}=\frac{-1}{-2}=\frac{1}{2}$
Usar punto $(-2,2)$ en $y=mx+b$: $2 = \frac{1}{2}(-2) + b$
Resolver $b$: $2 = -1 + b$ → $b=3$
Sustituir: $y = \frac{1}{2}x + 3$

Step7: Calcular pendiente y b (Preg8)

Puntos $(-3,-1)$ y $(-5,1)$
Calcular pendiente: $m=\frac{1 - (-1)}{-5 - (-3)}=\frac{2}{-2}=-1$
Usar punto $(-3,-1)$ en $y=mx+b$: $-1 = -1(-3) + b$
Resolver $b$: $-1 = 3 + b$ → $b=-4$
Sustituir: $y = -x - 4$

Answer:

1. $y = -9x - 4$
2. $y = \frac{3}{2}x - 4$
3. $y = -x - 2$
4. $y = 2x + 4$
5. $y = x - 1$
6. $y = -4x - 21$
7. $y = \frac{1}{2}x + 3$
8. $y = -x - 4$