A. False - 7/2 is more than 5/2 and the number line gets bigger as it goes up so 7/2 is above 5/2
B. True - the numbers get bigger as they go down on the negative side of the number line so -1 1/4 is above -1 3/4
C. and D are both False because the positive numbers are above the negative numbers
Hope that helps
Answer:
y=1/3x-3 2/3 (y equals one third times x minus three and two thirds)
Explanation:
Slope = rise (Δy) over run (Δx). Looking at the two points, (-1, -4) is furthest to the left. The x value increases by 3, and the y value increases by 1. That means slope = 1/3. Now, plug it into the slope equation y=mx+b, m being slope. We get y=1/3x+b. To find b (the y-intercept), plug in one of the points into the equation. So -4=1/3·(-1) +b. 1/3 times -1 is -1/3. Now we have -4=-1/3+b. -4-1/3= -11/3 (or negative 3 and 2/3). That means the y intercept is -3 2/3. Now we get the equation. y=1/3x-3 2/3
***Not sure which one you want to be solved but some of the ones with answers are wrong, so I will be explaining those as well with answers; the questions will be labeled 1-4 from top to bottom as shown in your picture***
#1.
Answer:
y=3x+4
Explanation:
The slope is 3 because every 1 unit to the right, the next point is increased by 3. In other words, the line rises 3 every 1 across. Slope is calculated by rise divided by run, in this graph the rise is 3 and the run is 1.
Slope= rise/run=3/1=3
The slope is not negative because it rises upwards from left to right; not downwards as a negative slope would.
Slope-intercept form is y=mx+b with m being slope, b being the y-intercept, and (x,y) being the set of points. The y-intercept is found as the point that intersects on the y axis, here being 4. So, the answer is y=3x+4.
#2.
Answer:
y=(1/2)x+3
Explanation:
Again, y-intercept form is y=mx+b. Here we are given the slope and the x-intercept(the y is 0). Because the slope is given, we can plug that in the slope-intercept equation right away:
y=(1/2)x+b
Now, we just need to find b. So, how can we solve for b? We need to make b the only variable in this equation. This can be done by plugging in the given point, (-6, 0). Here is how b is solved:
y=(1/2)x+b
0=(1/2)(-6)+b
0=-3+b
3=b
So, the equation is y=(1/2)x+3.
#3.
Answer:
y=3x+7
Explanation:
Two points are given. Slope can be found given two points and we can use the slope to create an equation in point-slope form, before solving for the slope-intercept form. Slope can be found using the equation:
m=(y2-y1)/(x2-x1)
This equation basically finds the rise and run of the slope before dividing to find the slope. Plugging in the points given for this problem and find slope is shown below: ((-2, 1) and (1, 10) are the points btw)
m=(10-1)/(1+2)
m=9/3
m=3
Now that we know the slope, we can pick one number to create point-slope form and then move the variables around to create slope-intercept form.
Point-slope form: (y-y1)=m(x-x1)
With variables: (y-1)=3(x+2)
Now, we can use this equation to create slope-intercept form:
(y-1)=3(x+2)
y-1=3x+6
y=3x+7 <—Final Answer!
#4.
Answer:
(y+2)=1/6(x-9)
Explanation:
Given the point and a slope, we can create the point-slope equation. (9,-2) and m=1/6 is given. Refer back to point slope form (y-y1)=m(x-x1). m is the slope and (x1, y1) is the point plugged in.
So, when you plug in the slope and the points you get (y+2)=1/6(x-9).
We need more info for this question...
Step-by-step explanation:
x varies inversely as y. This means that x is equal to the inverse of y which can be translated as x = 1/y but the problem said that x is <u>n</u><u>o</u><u>t</u><u> </u><u>e</u><u>x</u><u>a</u><u>c</u><u>t</u><u>l</u><u>y</u><u> </u><u>e</u><u>q</u><u>u</u><u>a</u><u>l</u><u> </u>to the inverse of y. Therefore, we need to introduce a factor k. Factor k will represent the word "varies" in the problem.
To illustrate:
Since we don't have the value of k, we have to solve for it by using the first values of x and y which was given as x=2 and y=20.
Now that we have the value of k, we can now solve for the value of x when y=5.
Therefore, when y is 5, the value of x is 8.
