Question

points (k+9,-4k-3) and (-2,1). y intercept of 9

Answer 1

What do you want to find with this data?

Answer 2

value of k and equation

Answer 3

@owlcoffee

Answer 4

Equation of what? line? circle?

Answer 5

equation in y=mx+b

Answer 6

That is called the equation of the line.
You see, we have to first calculate the slope of this line, which is calculated by the points given, of course, a y-intercept implies that the x-coordinate of the point is zero, so let's call the two points:
\[p(k+9, -4k-3)\]
\[m(0,9)\]
Where the point "m" is the y-intercept of the line, we want to calculate the slope using the formula \(m=\frac{ y_2-y_1 }{ x_2-x_1 }\) and jus plotting in the info:
\[m _{m,p}=\frac{ (-4k-3)-8 }{ (k+9)-0 }\]
yielding the result:
\[m _{m,p}=\frac{ -4k-11 }{ k+9 }\]
And pltting this to the form \((y-y_o)=m(x-x_o)\) where "m" is the slope we already calculated and we can replace yo and xo with any point we want:
\[(y-8)=\frac{ -4k-11 }{ k+9 }(x-0)\]
Further simplifying:
\[y=\frac{ -4k-11 }{ k+9 }x+8\]