Answer:
c = –13
Step-by-step explanation:
by property of tangent line, equation
x² – x – 12 = x + c
x² – 2x – 12 – c = 0
has only one solution, which mean
– 12 – c = 1
c = –13
Answer:
4y = 6x + 40
Step-by-step explanation:
The general equation of a straight line is y = mx + b
m is the slope and b is the y-intercept
let us write both equations in this form;
we have this as;
6y = -4x + 1
y = -4x/6 + 1/6
and;
2x + 3y = 18
3y = -2x + 18
y = -2x/3 + 6
So firstly we want to find an equation that is perpendicular to the first
When two lines are perpendicular, their slopes has a product of -1
The slope of the first line is -4/6
let the slope of the line we want be m
As per they are perpendicular;
-4/6 * m = -1
-4m/6 = -1
-4m = -6
m = 6/4
So now, we want the y-intercept greater than that of the second equation which is a y-intercept of 6
we can choose 10
and we have the equation as:
y = 6x/4 + 10
multiply through by 4
4y = 6x + 40
the function is increasing from x = 0 to x = 1
when x = 0, y = 2
when x = 1, y = 8
this shows an increase of +6, so we know this statement is true
we can see the rest are false simply because they state a decrease when there is an increase. this question is only confusing because we ask you about the increase and decrease in the function, when really its the same thing as asking about an increase or decrease in the y variable.
in other words, all youre looking for is the variation of the value of the y variable that is attached to the specific x variables.
hope this helps!!
