Find an equation of the line described below. Write the equation in slope-intercept form (solved for y), when possible.
Through (9,3 and (3,9)
What is the equation of the line?
To find the equation of the line, we can use the formula for slope, which is given by
m = (y2 - y1) / (x2 - x1),
where (x1, y1) = (9, 3) and (x2, y2) = (3, 9).
Plugging these values into the formula, we get:
m = (9 - 3) / (3 - 9)
= 6 / (-6)
= -1.
The slope of the line is -1.
We can now use the point-slope form of a line to find the equation. The point-slope form is given by:
y - y1 = m(x - x1),
where (x1, y1) = (3, 9) and m = -1.
Plugging in these values, we get:
y - 9 = -1(x - 3).
Expanding the equation, we get:
y - 9 = -x + 3.
To write the equation in slope-intercept form (solved for y), we can rearrange the equation:
y = -x + 3 + 9,
y = -x + 12.
Therefore, the equation of the line is y = -x + 12.