Question

What is an equation for the linear function whose graph contains the points (9,7) and (4,−8) ?

Enter your answers in the boxes.
y− = (x−9)

Answer 1

Answer:

Slope = (7 + 8)/(9 -4) = 15/5 = 3

equation

y - 7 = 3(x - 9)

hope it helps

Answer 2

y - 7 = 3(x-9)

Step-by-step explanation:

Consider the linear function is,

y = ax + b

if x = 9 and y = 7,

7 = a(9) + b

⇒ 9a + b = 7  ....(1)

if x = 4, y = -8,

-8 = a(4) + b

⇒ 4a + b = -8  ...(2)

Equation (1) - equation (2),

We get,

5a = 15

⇒ a = $\frac{15}{5}$ = 3,

From equation (1),

9(3) + b = 7

27 + b = 7

⇒ b = 7 - 27 = -20,

Hence, the required linear function,

y = 3x - 20

y = 3x - 27 + 7

y - 7 = 3(x-9)

Alternative method :

linear function is always a line,

Also, equation of a line passes through $(x_1, y_1)$ and $(x_2, y_2)$ is,

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Thus, the equation of line passes through (9, 7) and (4, -8),

$y-7=\frac{-8-7}{4-9}(x-9)$

$y-7=\frac{15}{5}(x-9)$

y - 7 = 3(x-9)

#Learn more :

What is linear function :

https://brainly.in/question/3709965