Mathematics: a line segment has the endpoint (2,-3) (-6,-1) Describe theOff the line that through the points ex and Y

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a line segment has the endpoint (2,-3) (-6,-1) Describe

kiekie1986

30.01.2022

Step-by-step explanation:

The point-slope form of an equation of a line:

y-y_1=m(x-x_1)

where the slope m is:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (2, -3) and (-6, -1).

Substitute:

$m=\dfrac{-1-(-3)}{-6-2}=\dfrac{2}{-8}=-\dfrac{1}{4}$

$y-(-3)=-\dfrac{1}{4}(x-2)\\\\y+3=-\dfrac{1}{4}(x-2)\to\text{point-slope form}$

The slope-intercept form of an equation of a line:

y=mx+b

$y+3=-\dfrac{1}{4}(x-2)$

$y+3=-\dfrac{1}{4}x+\dfrac{1}{2}$ subtract 3 from both sides

$y=-\dfrac{1}{4}x-2\dfrac{1}{2}\to\text{slope-intercept form}$

The standard form of an equation of a line:

Ax+By=C

$y+3=-\dfrac{1}{4}(x-2)$ multiply both sides by 4

4y+12=-(x-2)

4y+12=-x+2 subtract 12 from both sides

4y=-x-10 add x to both sides

$x+4y=-10\to\text{standard form}$

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