The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-2, 3) and (1, -3). Substitute:
[tex]m=\dfrac{-3-3}{1-(-2)}=\dfrac{-6}{3}=-2\\\\y-(-3)=-2(x-1)\\\\y+3=-2(x-1)[/tex]
The standard form: Ax + By = C. Convert:
[tex]y+3=-2(x-1)[/tex] use distributive property
[tex]y+3=-2x+2[/tex] subtract 3 from both sides
[tex]y=-2x-1[/tex] add 2x to both sides
[tex]\boxed{2x+y=-1}\to\boxed{c.}[/tex]
Answer:
b
Step-by-step explanation:
You can determine the gradient from the two points (-2, 3) and (1, -3). The gradient of a straight line is:
[tex]m=(y_2-y_1)/(x_2-x_1)[/tex]
[tex]m=(-3-3)/(1-(-2))=-6/3=-2[/tex]
The equation for a straight line is:
[tex]y=m\cdot{x}+c[/tex]
c is the y-intercept when x=0. We can substitute any point into the equation. Lets use point 1 and solve for c .
[tex]3=-2\cdot{-2}+c[/tex]
[tex]c=-1[/tex]
The equation is:
[tex]y=-2\cdot{x}-1[/tex]
The answer is b
