Draw the graphs of the functions y=1.2x+.9 and y=−1.3x+4.4. Using the graph, locate the points of intersection of the two graphs
. Now find the exact y and x coordinates of the point of intersection (use algebra).
1 answer:
To draw a graph of any linear function you need two points only. We usually use x and y intercepts because these are easiest to work with.
To find x-intercept we set y to be 0. This is also called zero of a function. Let us find x-intercepts for those two functions:
Now we simply set y=0 and solve for x:
Now we need to find y-intercepts. To do this we simply set x to be zero.
Graphs of our functions are not defined by these two points.
To draw a graph you simply draw a line through these two points.
To find intersection we can use a fact that at the point of intersection both functions have the same value. We can write that down mathematically this way:
-1.3x+4.4=1.2x+0.9
Now we need to solve for x. This will give us an x coordinate of the intersection point.
Now we simply plug in these value of x in any function to obtain y coordinate of the interception point.
Our intersection point the following coordinates (1.4,2.6).
I have attached the graph with all the points that we calculated highlighted.
To find x-intercept we set y to be 0. This is also called zero of a function. Let us find x-intercepts for those two functions:
Now we simply set y=0 and solve for x:
Now we need to find y-intercepts. To do this we simply set x to be zero.
Graphs of our functions are not defined by these two points.
To draw a graph you simply draw a line through these two points.
To find intersection we can use a fact that at the point of intersection both functions have the same value. We can write that down mathematically this way:
-1.3x+4.4=1.2x+0.9
Now we need to solve for x. This will give us an x coordinate of the intersection point.
Now we simply plug in these value of x in any function to obtain y coordinate of the interception point.
Our intersection point the following coordinates (1.4,2.6).
I have attached the graph with all the points that we calculated highlighted.
You might be interested in
Answer:
- arc BF = 76°
- ∠M = 31°
- ∠BGE = 121°
- ∠MFB = 111°
Step-by-step explanation:
(a) ∠FBM is the complement of ∠FBC, so is ...
∠FBM = 90° -52° = 38°
The measure of arc BF is twice this angle, so is ...
arc BF = 2∠FBM = 2(38°)
arc BF = 76°
__
(b) ∠M is half the difference between the measures of arcs BE and BF, so is ...
∠M = (1/2)(138° -76°) = 62°/2
∠M = 31°
__
(c) arc FC is the supplement to arc BF, so has measure ...
arc FC = 180° -arc BF = 180° -76° = 104°
∠BGE is half the sum of arcs BE and FC, so is ...
∠BGE = (1/2)(arc BE +arc FC) = (138° +104°)/2
∠BGE = 121°
__
(d) ∠MFB is the remaining angle in ∆MFB, so has measure ...
∠MFB = 180° -∠M -∠FBM = 180° -31° -38°
∠MFB = 111°
It depends on how b approaches 0
If b is positive and gets closer to zero, then we say b is approaching 0 from the right, or from the positive side. Let's say a = 1. The equation a/b turns into 1/b. Looking at a table of values, 1/b will steadily increase without bound as positive b values get closer to 0.
On the other side, if b is negative and gets closer to zero, then 1/b will be negative and those negative values will decrease without bound. So 1/b approaches negative infinity if we approach 0 on the left (or negative) side.
The graph of y = 1/x shows this. See the diagram below. Note the vertical asymptote at x = 0. The portion to the right of it has the curve go upward to positive infinity as x approaches 0. The curve to the left goes down to negative infinity as x approaches 0.
Answer:
d. y = -2×
Step-by-step explanation:
First to solve find the slope using the formula, . The slope equals 20/-10 or -2. Then plug the slope and point, (-5,10), into slope-point form. y-10=-2(x+5), then solve for y. This gives you y=-2x+0 or y=-2x.