Question

Choose the equation that represents a line that passes through points (-1, 2) and (3, 1).

Answer 1

Answer:

b.) x + 4y = 7

Step-by-step explanation:

when x = -1    and y = 2   :  -1+4(2) = -1 +8 = 7 .....right

when x = 3    and y = 1  : 3+4(1) = 7 .....right

Answer 2

Answer:

b

Step-by-step 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, 2) and (x₂, y₂ ) = (3, 1)

m = $\frac{1-2}{3+1}$ = - $\frac{1}{4}$, thus

y = - $\frac{1}{4}$ x + c ← is the partial equation

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

Using (- 1, 2), then

2 = $\frac{1}{4}$ + c ⇒ c = 2 - $\frac{1}{4}$ = $\frac{7}{4}$

y = - $\frac{1}{4}$ x + $\frac{7}{4}$ ← in point- slope form

Multiply through by 4

4y = - x + 7 ( add x to both sides )

x + 4y = 7 → b