Question

Write the equation of the line that passes through (1, 5) and (−2, 14) in the slope-intercept form.

a- y = 3x + 2
b- y = 3x + 8
c-y = −3x − 2
d- y = −3x + 8

Answer 1

D. Y=-3x+8

Explanation:

SLOPE FORMULA:

y₂-y₁/x₂-x₁=rise/run

SLOPE-INTERCEPT FORM:

Y=MX+B

m represents the slope.

b represents the y-intercept.

y₂=14

y₁=5

x₂=(-2)

x₁=1

14-5/(-2)-1

14-5 (Solve.)

14-5=9

(-2)-1=(-3)

9/-3=(-3)

The slope is (-3).

The y-intercept is 8.

y=-3x+8

As a result, the final answer is (D.) y=-3x+8.

Answer 2

d

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, 5) and (x₂, y₂ ) = (- 2, 14)

m =
`(14-5)/(-2-1)` =
`(9)/(-3)` = - 3, thus

y = - 3x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (1, 5), then

5 = - 3 + c ⇒ c = 5 + 3 = 8

y = - 3x + 8 → d