Answer:
B.) x + 4y = 7
Explanation:
(Step 1) ----------------------------------------------------------------------------------------------
To find the equation, we first need to find the slope using the point-slope form:
y₁ - y₂ = m(x₁ - x₂)
In this form, "m" represents the slope, "x₁" and "y₁" represent the values from the first point, and "x₂" and "y₂" represent the values from the second point.
Point 1: (-1, 2) Point 2: (3, 1)
x₁ = -1 x₂ = 3
y₁ = 2 y₂ = 1
y₁ - y₂ = m(x₁ - x₂) <----- Point-slope form
2 - 1 = m(-1 - 3) <----- Insert values
1 = m(-4) <----- Subtract
-1/4 = m <----- Divide both sides by -4
(Step 2) ---------------------------------------------------------------------------------------------
The given equations are in the slope-intercept form. The general structure looks like this:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept. To find the y-intercept, you can plug the newfound slope and values from one point into the equation.
x = -1
y = 2
m = -1/4
y = mx + b <----- Slope-intercept form
2 = (-1/4)(-1) + b <----- Insert values
2 = 1/4 + b <----- Multiply -1/4 and -1
8/4 = 1/4 + b <----- Make common denominators
7/4 = b <----- Subtract both sides by 1/4
(Step 3) ---------------------------------------------------------------------------------------------
The equation in slope-intercept form is thus: y = -1/4x + 7/4.
While this equation is accurate, it seems that it must be slightly manipulated. Therefore, we need to alter this equation to look like one of the answer choices. For instance, we can multiply the entire equation by 4 to remove the denominator.
y = -1/4x + 7/4 <----- Equation
4y = -x + 7 <----- Multiply all terms by 4
x + 4y = 7 <----- Add "x" to both sides