Question

How do you find the general form of the line that passes through point A(-6, 8); x-intercept 2?

Answer 1

The equation of the line is `y= -x+2`

Explanation:

The coordinate of x-intercept is `(2,0)`The slope of the line is `(8-0)/(-6-2)=-1`.The equation of the line passing through pt `A (-6,8)` having a slope of `-1` is `y-8=-1(x+6) ory-8=-x-6or y= -x+2` graph{-x+2 [-10, 10, -5, 5]}[Ans]

Answer 2

`y=-x+2`

Explanation:

`color(red)("Assumption: This question is based on a straight line")`

The standard form of this equation type is:`" "y=mx+c`

Where `m` is the gradient and `c` is the y intercept

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`color(blue)("To determine the gradient")`

The x-intercept is at `y=0`

Let point `P_1` be the x-intercept

Then `P_1->(x_1,y_1)=(2,0)`

We are given a point A
Let point `P_A->(x_A,y_A)=(-6,8)`

`color(brown)("It is not good practice to change the lettering in a question.")` `color(brown)("It makes a lot of work for the person marking your solution")`

The gradient is `("change in y")/("change in x")=m`

`=>m->P_A-P_1-> ("change in y")/("change in x")= (y_A-y_1)/(x_A-x_1`

`=> m=(8-0)/(-6-2)=8/(-8)=-1`

`color(green)("So the equation is now "y=-x+c)`
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`color(white)(.)`

`color(blue)("Determine the value of "c)`

The line passes through `P_A->(x,y)=(-6,8)`

So by substitution we have

`8=-(-6)+c`

`=>8=+6+c`

Subtract 6 from both sides

`=>c=2`

`color(green)("So the equation is now "y=-x+2)`