Find an equation of the line described below. Write the equation in slope-intercept form (solved for y), when possible.
Through (11,3) and (3,11)
What is the equation of the line?
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(Simplify your answer.)
First, let's find the slope of the line using the formula:
slope = (change in y) / (change in x)
Given the points (11,3) and (3,11), the change in y is 11 - 3 = 8 and the change in x is 3 - 11 = -8.
So, the slope of the line is:
slope = 8 / -8 = -1
Now, let's find the y-intercept using the point-slope form of a line, which is:
y - y₁ = m(x - x₁)
Using the point (11,3) and the slope -1, we have:
y - 3 = -1(x - 11)
y - 3 = -x + 11
Finally, let's solve for y:
y = -x + 11 + 3
y = -x + 14
Therefore, the equation of the line in slope-intercept form is y = -x + 14.