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Sagot :
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:
[tex]\begin{gathered} y\text{ = mx + b} \\ m\text{ = slope, b = y-intercept} \end{gathered}[/tex]The slope formula is given as:
[tex]$m\text{ = }\frac{y_2-y_1}{x_2-x_1}$[/tex][tex]\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}[/tex]To get the y-intercept, we will use any of the given points and the slope
[tex]\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}[/tex]Next substitute the slope and y-intercept
[tex]\begin{gathered} y\text{ = 1\lparen x\rparen + \lparen-5\rparen} \\ \\ The\text{ equation od the line becomes:} \\ y\text{ = x - 5} \\ \end{gathered}[/tex]
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