Question

Find the slope then write an equation for the line that passes through each pair of points (5, 6), (-10, – 15)

Answer 1

The given points are,

x1, y1 = 5, 6

x2, y2 = -10, -15

The general line equation is,

y = mx +b

Here, m is the slope and b is the y intercept.

The slope m can be calculated as,

$m=\frac{y2-y1}{x2-x1}=\frac{-15-6}{-10-5}=\frac{21}{15}$

Now, b can be calculated by taking a point and susbtituting the values in the line equation.

Let us here take, th points (5,6). Therefore we have,

$\begin{gathered} 6=\frac{21}{15}\times5+b \\ 6=7+b \\ b=-1 \end{gathered}$

Thus, the equation is,

$y=\frac{21}{15}x-1$