Creating the Equation of a Line
The slope-intercept form of a line is expressed as:
y = mx + b
- m = slope of the line
- b = y-intercept of the line
Given:
- The point (6, 1)
- The slope m = 4
We can substitute the given slope and the coordinates of the point into the slope-intercept form to find the value of b:
Using the point (6, 1) where:
- x = 6
- y = 1
Now, substituting into the equation:
1 = 4(6) + b
1 = 24 + b
To find b, we solve for it:
b = 1 – 24
b = -23
Now that we have the value of b, we can write the final equation by substituting the slope and y-intercept back into the slope-intercept form:
y = 4x – 23
This means the equation of the line that passes through the point (6, 1) with a slope of 4 is:
Final Equation:
y = 4x – 23