Question

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.)

Answer 1

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.