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.