Find all solutions to the system: 5x-3y=2, 15x+6y=6
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Answer:
We are given the table of a linear function
Since we have to find the equation of the function in the slope-intercept form,
we require the slope as well as the y-intercept
<u>Finding the slope:</u>
We know that slope of a line is Rise / Run
Since from the graph, we notice that the difference of 2 consecutive x-coordinates is 1
Hence, we have the x-coordinates at an interval of 1 and since the slope of a line is defined as the units ascended by the line after covering 1 unit in the x-coordinate
change in y = y - y
(where n is the number of row in the table)
change in y = 31 - 23
change in y = 8 = Rise
Run = 1 (Since the interval in the table is 1)
Slope = Rise / Run
Slope = 8 / 1
Slope = 8
<u>Finding the y-intercept:</u>
We need the y-coordinate at x = 0
Going up from the third row, we notice that for every unit decreased in the x-coordinate , 8 units of the y-coordinate are decreased (since the slope =8)
In that case, the y-coordinate of every decreased x-coordinate will be 8 less than the last one
so we can say that the y-coordinate of x = 1 will be 8 less than 23 since x=1 is one less than x = 2
similarly, we can also say that the y-coordinate of x = 0 will be 8 less than (23-8) since x = 0 is one less than x = 1
Therefore, the y-coordinate at x =0
y = (23-8-8)
y-intercept = 7
<u>Making the Equation:</u>
We need to write the equation in the form:
y = ax + b (where a is the slope of the line and b is the y-intercept)
Replacing the known values, we get
y = 8x + 7
Therefore, the equation of the formula shown in the table is y = 8x + 7