Find an equation of the line described below. Write the equation in slope-intercept form (solved for y), when possible.
through (14,10) and (10,14)
What is the equation of the line?
To find the equation of the line, we first need to find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (14, 10) and (x2, y2) = (10, 14).
m = (14 - 10) / (10 - 14) = 4 / -4 = -1
Now that we know the slope (m), we can use the point-slope form of a line:
y - y1 = m(x - x1)
Using either of the given points, let's use (14, 10):
y - 10 = -1(x - 14)
Next, we can simplify and rewrite it in slope-intercept form (solved for y):
y - 10 = -x + 14
y = -x + 24
The equation of the line is y = -x + 24.