Question

y 12 11 10 9 7 6 5 4 3 2 1 12-11-10 9 8 7 6 5 -4 -3 1 4 5 7 8 9 10 11 12 -1 -9

Answer 1

Question:

Solution.

The slope-intercept form of a line is given by the following formula:

$y\text{ = mx + b}$

where m is the slope of the line and b is the y-coordinate of the y-intercept. Now, by definition, the slope of a line is given by the following equation:

$m\text{ = }\frac{Y2-Y1}{X2-X1}$

where (X1,Y1) and (X2,Y2) are points on the line. For example, in the given line, take the points:

(X1,Y1) = (-2,0)

(X2,Y2) = (0,-6)

then, the slope m of the given line is :

$m\text{ = }\frac{Y2-Y1}{X2-X1}=\text{ }\frac{-6-0}{0-(-2)}=\text{ }\frac{-6}{2}\text{ = -3}$

then, for now, the equation of the given line is

y = -3x+ b

now, to find b, take any point (x,y) on the line, replace it on the above equation and solve for b. For example, take (x,y) = (0,-6) then, we get:

-6 = 3(0) + b

thus

b = -6.

Then, replacing the b and m obtained above into the slope-intercept form of a line, we obtain that the equation of the given line is:

y = -3x -6

then, we can conclude that the correct solution is:

$y\text{ = -3x -6}$