Graph of a linear equation with points (1, -1) and (4, 3) plotted.

Let’s find the equation of the line that passes through the two points: (1, -1) and (4, 3).

Step 1: Find the slope (m) of the line.

The formula for slope between two points (x₁, y₁) and (x₂, y₂) is:

m = (y₂ - y₁) / (x₂ - x₁)

Plug in the values:

x₁ = 1, y₁ = -1
x₂ = 4, y₂ = 3

So,

m = (3 - (-1)) / (4 - 1)
m = (3 + 1) / 3
m = 4 / 3

Step 2: Use point-slope form to write the equation.

Point-slope form is:

y - y₁ = m(x - x₁)

We can use either point. Let’s use (1, -1):

y - (-1) = (4/3)(x - 1)
→ y + 1 = (4/3)(x - 1)

Step 3: Convert to slope-intercept form (y = mx + b).

Distribute the 4/3:

y + 1 = (4/3)x - 4/3

Subtract 1 from both sides:

y = (4/3)x - 4/3 - 1

Convert 1 to thirds: 1 = 3/3

y = (4/3)x - 4/3 - 3/3
y = (4/3)x - 7/3

✔ Double-check with the other point (4, 3):

Plug x = 4 into the equation:

y = (4/3)(4) - 7/3 = 16/3 - 7/3 = 9/3 = 3 → Correct!

Final Answer:
y = \frac{4}{3}x - \frac{7}{3}