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Romashka
2 months ago
15

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).

Mathematics
1 answer:
babunello [11.8K]2 months ago
7 0
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:
y=1.2x+0.9
y=-1.3x+4.4
Now, we simply assign y=0 and solve for x:
0=1.2x+0.9
0=-1.3x+4.4

1.2x=-0.9
1.3x=4.4

x=-0.75
x=3.4
Next, we need to ascertain y-intercepts. To achieve this, we set x to zero.
y=1.2x+0.9
y=-1.3x+4.4

y=0.9
y=4.4
The graphs of these functions are defined by these two points.
y=1.2x+0.9; (0,-0.75),(0.9,0)
y=-1.3x+4.4; (0,3.4),(4.4,0)
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.
2.5x=3.5
x=1.4
Next, we substitute this x value into any function to find the y-coordinate of the intersection point.
y=1.2x+0.9
y=1.2(1.4)+0.9
y=2.6
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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Required:

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