Question

Write a linear equation that passes through the two points (-6, -7) and (3, -4).

Answer 1

linear equation that passes through the two points (-6, -7) and (3, -4) is $y=\frac{1}{3}x-5$

Step-by-step explanation:

We need to write the equation that passes through the two points (-6, -7) and (3, -4).

The equation can be written is point slope form.

The standard form of point slope equation is:

$y=mx+b$

where m is the slope and b is the y-intercept

Finding slope m:

Slope can be found by using formula:

$slope = \frac{y_{2}-y_{1}}{x{2}-x_{1}} \\Where\,\, y_{2}=-4,y_{1}=-7,x{2}=3,x_{1}=-6\\slope =\frac{-4-(-7)}{3-(-6)}\\slope=\frac{-4+7}{3+6}\\slope=\frac{3}{9}\\slope=\frac{1}{3}$

So, slope is $\frac{1}{3}$

Now finding y-intercept b

Putting slope $\frac{1}{3}$ and point(-6,-7)

$y=mx+b\\x=-6,y=-7,m=\frac{1}{3} \\-7=\frac{1}{3}(-6)+b\\-7=-2+b\\b=-7+2\\b=-5$

So, value of b is -5

Putting values to find the equation:

$y=mx+b\\m=\frac{1}{3} and b=-5\\y=\frac{1}{3}x-5$

So, linear equation that passes through the two points (-6, -7) and (3, -4) is $y=\frac{1}{3}x-5$

Keywords: Linear Equation,

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