Question

How do you write an equation of a line given (-5,9) and (-4,7)?

Answer 1

The equation of the line in standard form is `2x +y = -1`

Explanation:

The slope of the line passing through `(-5,9) and (-4,7)` is `m= (y_2-y_1)/(x_2-x_1)= (7-9)/(-4+5)=-2/1= -2`

Let the equation of the line in slope-intercept form be `y=mx+c or y= -2x+c`

The point (-5,9) will satisfy the equation . So, `9= -2*(-5)+c or c= 9-10= -1`

Hence the equation of the line in slope-intercept form is `y= -2x-1.`

The equation of the line in standard form is `2x +y = -1` [Ans]

Answer 2

Given two points `(x_1,y_1)` and `(x_2,y_2)`
the slope can be calculated as
`color(white)("XXX")m=(y_2-y_1)/(x_2-x_1)`
and
once we have a slope, `m`
we can write an equation for the line in slope-point form as either
`color(white)("XXX")y-y_1=m(x-x_1)`
or
`color(white)("XXX")y-y_2=m(x-x_2)`

Using `(x_1,y_1)=(-5,9)` and `(x_2,y_2)=(-4,7)`
`color(white)("XXX")m=(7-9)/((-4)-(-5))=-2`
and
an equation for this line can be written as
`color(white)("XXX")y-9=(-2)(x-(-5))`

While this is a completely valid answer, we would normally simplify this and (perhaps) re-write it in "standard" form:
`color(white)("XXX")y-9=-2x-10`

`color(white)("XXX")2x+y=-1`

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It would be a good idea to verify that this equation is valid for the two given points, so:
`{: ("Substituting: "(-5,9)" for " (x,y),color(white)("xxxxxx"),"Substituting: "(-4,7)" for " (x,y)), (" in " 2x+y=-1,," in " 2x+y=-1), ("",,""), (rarr2*(-5)+9=-1,,rarr2*(-4)+7=-1), ("correct",,"correct") :}`