Question

what is an equation of the line that passes through the points (4, -3) and (2, -4)?
answer attempt 1 out of 2
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Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For the points \((4, - 3)\) and \((2, - 4)\), we have \( x_1 = 4,y_1=-3,x_2 = 2,y_2=-4 \). So \( m=\frac{-4-(-3)}{2 - 4}=\frac{-4 + 3}{-2}=\frac{-1}{-2}=\frac{1}{2} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Let's use the point \((4,-3)\) (we could also use \((2,-4)\)). Substitute \( m=\frac{1}{2},x_1 = 4,y_1=-3 \) into the point - slope form: \( y-(-3)=\frac{1}{2}(x - 4) \).
Simplify this equation: \( y + 3=\frac{1}{2}x-2 \). Then, subtract 3 from both sides to get the slope - intercept form: \( y=\frac{1}{2}x-2 - 3=\frac{1}{2}x-5 \). We can also write it in standard form. Multiply through by 2 to get \( 2y=x - 10 \), or \( x-2y=10 \). But the slope - intercept form \( y=\frac{1}{2}x - 5 \) is also a correct equation of the line.

Answer:

\( y=\frac{1}{2}x - 5 \) (or other equivalent forms like \( x - 2y=10 \) or \( y+3=\frac{1}{2}(x - 4) \))