Question

What is an equation of the line that passes through the points (-1, -6), (6,1)?

Answer 1

Answer:

y = x - 5

Explanation:

Given:

The points are (-1, -6) and (6, 1)

To find:

the equation of line that pass through the points

To determine the equation of the line, it will be in the form:

$\begin{gathered} y\text{ = mx + b} \\ m\text{ = slope, b = y-intercept} \end{gathered}$

The slope formula is given as:

$m\text{ = }\frac{y_2-y_1}{x_2-x_1}$$\begin{gathered} x_1=-1,y_1=-6,x_2=6,y_2\text{ = 1} \\ m\text{ = }\frac{1-(-6)}{6-(-1)} \\ m\text{ = }\frac{1+6}{6+1}=\text{ }\frac{7}{7} \\ m\text{ = 1} \end{gathered}$

To get the y-intercept, we will use any of the given points and the slope

$\begin{gathered} Using\text{ point \lparen6, 1\rparen: x = 6, y = 1} \\ y\text{ = mx + b} \\ 1\text{ = 1\lparen6\rparen + b} \\ 1\text{ = 6 + b} \\ 1-6\text{ = b} \\ b\text{ = -5} \end{gathered}$

Next substitute the slope and y-intercept

$\begin{gathered} y\text{ = 1\lparen x\rparen + \lparen-5\rparen} \\ \\ The\text{ equation od the line becomes:} \\ y\text{ = x - 5} \\ \end{gathered}$