Answer:
a) For a constant increment in x-variable, there is a constant increment in y-variable, for example, for x = 0 to x = 0.5 (increment = 0.5) y-variable goes from 60 to 62 (increment = 2); the same is valid for any couple of (x,y) values. This behaviour is characteristic of linear equations.
b) slope:
m = (increment in y-variable)/(increment in x-variable) = 2/0.5 = 4
y-intercept:
y1 = m*x1 + h
60 = 4*0 + h
60 = h
equation: y = 4x + 60
where y represents scores and x represents hours spent studying
c) The slope indicates that you need to study 1 hour to increase your score in 4 points
The y-intercept indicates that you will get at least a score of 60, even though you hadn't studied
X=24
Work: x-10=14 x=14+10
Your neighbor will let you take water from the well on his claim,
charging you $.05 a quart.
If 'x' is the number of quarts you take from his well on Tuesday, then
'y' is the amount of money you owe him before the sun goes down.
1) y=3x-4
When x increases by 1, y increases by 3 so the slope is rise/run → 3
y-int is -4 bc y-value is -4 when x=0
2)y=-3x+4
When x increase by 2, y decreases by 6 so the slope is rise/run → -3
y-int is 4 bc y-value is 4 when x=0
3)y=-1/3x+4
When x increase by 3, y decreases by 1 so the slope is rise/run → -1/3
y-int is 4 bc you now have the equation y=-1/3x+b and u just have to plug in random point from the graph, so ex, 6 into x and 2 into y. You can get 4 as b in the equation.
4)y=1/3x-4
When x increases by 6, y decreases by 2 so the slope is rise/run → 1/3
y-int is -4 bc u do the same thing as 3)
For ex, plug in 6 for x and -2 for y and you can get -4 as the b in the equation.
The equation of the tangent to the curve at the point P(2, -10) is:
y = 8x - 26
We need to find the coordinates of point Q where the slope of the tangent to the curve f(x) must also be 8.
Now we have a quadratic:
which simplifies to:
which factorizes to:(x + 4)(x - 2) = 0
Therefore x = -4, 2.
f(-4) = 48
Therefore the coordinates of Q are (-4, 48).
