A Point-Slope equation of a straight line has this form: y - y1 = m(x-x1)
We can recognize any points of the graph.
(0,80000) ; (10,50000)
Given:
<span>y -50,000 =______(x -10)
We need to find the slope.
Slope = Change in y / Change in x = 80,000 - 50,000 / 0 - 10 = 30,000 / -10 = -3,000
The slope is equal to -3000. Choice A.
</span><span>y -50,000 = -3,000(x -10)</span>
3 is in the hundreds place, therefore 3 hundreds or 300
let x = the distance from Delany's house to the mall
so half the distance would be 1/2x
then it is 5 miles less than that so you would subtract 5 to give you 1/2x-5
and that is more than 6 miles so you get 1/2x-5>6
The simple/ <span>common sense method:
</span>The typical lay out of a quadratic equation is ax^2+bx+c
'c' represents where the line crosses the 'y' axis.
The equation is only translated in the 'y' (upwards/downwards) direction, therefore only the 'c' component of the equation is going to change.
A translation upwards of 10 units means that the line will cross the 'y' axis 10 places higher.
9+10=19,
therefore <u>c=19</u>.
The new equation is: <u>y=x^2+19 </u>
<span>
<span>The most complicated/thorough method:
</span></span>This is useful for when the graph is translated both along the 'y' axis and 'x' axis.
ax^2+bx+c
a=1, b=0, c=9
Find the vertex (the highest of lowest point) of f(x).
Use the -b/2a formula to find the 'x' coordinate of your vertex..
x= -0/2*1, your x coordinate is therefore 0.
substitute your x coordinate into your equation to find your y coordinate..
y= 0^2+0+9
y=9.
Your coordinates of your vertex f(x) are therefore <u>(0,9) </u>
The translation of upward 10 units means that the y coordinate of the vertex will increase by 10. The coordinates of the vertex g(x) are therefore:
<u>(0, 19) </u>
substitute your vertex's y coordinate into f(x)
19=x^2+c
19=0+c
c=19
therefore <u>g(x)=x^2+19</u>
Answer:
The fourth choice.
Step-by-step explanation:
Because since 90 miles is basically counted as your first day, you do the number of days, n, minus 1 and then multiply it by 5 to find the number of miles walked after the first day. Then you add it to 90.
