Question

find an equation for the line that passes through the points (-5, 1) and (5, 6).

Explanation:

Step1: Calculate the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \((x_1,y_1)=(-5,1)\) and \((x_2,y_2)=(5,6)\). So, \(m=\frac{6 - 1}{5 - (-5)}=\frac{5}{10}=\frac{1}{2}\).

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 \((-5,1)\) and \(m = \frac{1}{2}\). Substitute into the formula: \(y - 1=\frac{1}{2}(x - (-5))\), which simplifies to \(y - 1=\frac{1}{2}(x + 5)\).

Step3: Convert to slope - intercept form

Expand the right - hand side: \(y - 1=\frac{1}{2}x+\frac{5}{2}\). Then add 1 to both sides. Since \(1=\frac{2}{2}\), we have \(y=\frac{1}{2}x+\frac{5}{2}+\frac{2}{2}=\frac{1}{2}x+\frac{7}{2}\).

Answer:

\(y=\frac{1}{2}x+\frac{7}{2}\)