Find an equation of the line described below. Write the equation in slope-intercept form (solved for y), when possible.
Through (13,5) and (5,13)
What is the equation of the line?
To find the equation of the line in slope-intercept form, we need to determine the slope (m) and the y-intercept (b).
The formula to find the slope (m) is:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (13,5) and (5,13), we can substitute these values into the formula:
m = (13 - 5) / (5 - 13) = -8 / -8 = 1
Now that we have the slope (m), we can choose any of the given points and substitute the values into the formula:
y = mx + b
5 = 1(13) + b
To solve for b, we can simplify the equation:
5 = 13 + b
b = 5 - 13
b = -8
Now that we have the slope (m) and the y-intercept (b), we can write the equation of the line:
y = mx + b
y = 1x - 8
y = x - 8
Therefore, the equation of the line is y = x - 8.