How to Find the Equation of a Line Given a Slope and a Point?

To find the equation of a line with a given slope and a specific point, we can use the point-slope form of the equation of a line. The point-slope form is expressed as:

y – y₁ = m(x – x₁)

Where:

• m is the slope of the line.
• (x₁, y₁) is the given point that the line passes through.

In this problem, we are given:

• Slope (m) = 4
• Point (x₁, y₁) = (6, 11)

Now we will substitute the slope and the point into the point-slope formula:

y – 11 = 4(x – 6)

Next, we can simplify this equation to find the slope-intercept form of the line (y = mx + b):

1. Distribute the slope (4) on the right side:

    y – 11 = 4x – 24

2. Add 11 to both sides to isolate y:

    y = 4x – 24 + 11

    y = 4x – 13

So, the equation of the line with a slope of 4 that passes through the point (6, 11) is:

y = 4x – 13