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 graph any linear function, only two points are needed. We typically utilize x and y intercepts because they are the simplest to handle.
To calculate the x-intercept, we set y to 0, also known as the function's zero. Let's determine the x-intercepts for these two functions:
Now, we simply assign y=0 and solve for x:
Next, we need to ascertain y-intercepts. To achieve this, we set x to zero.
The graphs of these functions are defined by these two points.
To sketch the graph, simply draw a line connecting these two points.
To find the intersection, we utilize the fact that at the intersection point, both functions have the same value. This can be expressed mathematically as:
-1.3x+4.4=1.2x+0.9
Now, we solve for x to determine the x-coordinate of the intersection point.
Next, we substitute this x value into any function to find the y-coordinate of the intersection point.
The intersection point's coordinates are (1.4,2.6).
I have provided the graph with all the highlighted points we calculated.
To calculate the x-intercept, we set y to 0, also known as the function's zero. Let's determine the x-intercepts for these two functions:
Now, we simply assign y=0 and solve for x:
Next, we need to ascertain y-intercepts. To achieve this, we set x to zero.
The graphs of these functions are defined by these two points.
To sketch the graph, simply draw a line connecting these two points.
To find the intersection, we utilize the fact that at the intersection point, both functions have the same value. This can be expressed mathematically as:
-1.3x+4.4=1.2x+0.9
Now, we solve for x to determine the x-coordinate of the intersection point.
Next, we substitute this x value into any function to find the y-coordinate of the intersection point.
The intersection point's coordinates are (1.4,2.6).
I have provided the graph with all the highlighted points we calculated.
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Answer: 11, 13
Explanation:
We need to identify two consecutive integers whose product is 143. If we let x represent the larger of the two integers, the smaller integer can be expressed as (x-2). Their product equals 143, which gives us
By solving the equation:
this results in a second-order equation with two real roots: x=13 and x=-11. We disregard the negative outcome, leaving us with x=13. Hence, the two numbers are
x=13
x=13-2=11
We apply the slope formula by substituting the given points.
Here, x2 equals 5 and x1 equals -2; y2 equals -3 and y1 equals 6.
Thus, the line's slope is -9 divided by 7.