Find an equation of the line described below. Write the equation in slope-intercept form (solved for y), when possible.
Through (7, 3) and (3, 7)
____
What is the equation of the line? (Simplify your answer.)
To find the equation of the line, we can use the formula for finding the slope of a line:
m = (y2 - y1)/(x2 - x1)
Using the coordinates (7, 3) and (3, 7), we can substitute the values into the formula:
m = (7 - 3)/(3 - 7)
m = 4/-4
m = -1
Now that we have the slope, we can use the point-slope form of a line to write the equation:
y - y1 = m(x - x1)
Using the point (7, 3) as our point (x1, y1), we substitute the values:
y - 3 = -1(x - 7)
Simplifying the equation, we get:
y - 3 = -x + 7
Adding x to both sides:
y = -x + 7 + 3
Simplifying further, we get the equation in slope-intercept form:
y = -x + 10