What is the equation of a line that goes through the point (9, 3) with a slope of 6?

To find the equation of a line that passes through a specific point and has a given slope, we can use the point-slope form of the equation of a line. The point-slope form is represented as:

y – y₁ = m(x – x₁)

where:

• (x₁, y₁) is a point on the line,
• m is the slope of the line.

In this case, the point given is (9, 3), which means:

• x₁ = 9
• y₁ = 3
• m = 6

Now, we can substitute these values into the point-slope formula:

y – 3 = 6(x – 9)

Next, we can simplify the equation:

y – 3 = 6x – 54

To isolate y, add 3 to both sides:

y = 6x – 54 + 3

y = 6x – 51

Thus, the equation of the line that passes through the point (9, 3) and has a slope of 6 is:

y = 6x – 51

This equation can be used to determine the y-coordinate of any point on the line when the x-coordinate is known. It effectively describes the relationship between x and y for the given slope and point.