Problem

Find the equation of the line that passes through the points (4, -3) and (2, -1) using the point-slope form.

Answer

Expert–verified
Hide Steps
Answer

Simplify the equation to get the final result, \(y + 3 = -x + 4\), or rearrange it to standard form, \(x + y = 1\)

Steps

Step 1 :First, we should find the slope of the line that passes through the points (4, -3) and (2, -1). The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Step 2 :Substituting the given points into the formula, we get \(m = \frac{-1 - (-3)}{2 - 4} = \frac{2}{-2} = -1\)

Step 3 :Now we can use the point-slope form of the equation of a line, which is \(y - y_1 = m(x - x_1)\)

Step 4 :Choose one of the points to substitute into the equation, for instance, (4, -3), we get \(y - (-3) = -1(x - 4)\)

Step 5 :Simplify the equation to get the final result, \(y + 3 = -x + 4\), or rearrange it to standard form, \(x + y = 1\)

link_gpt