The value of the function g(x) is −2 when x=−5 and is 5.7 when x=6. What is the equation for the function g(x)?
ik im rly late and no offense oobleck and ashley but those answers rly don't help at all
To find the equation for the function g(x), we can use the two given points: (-5, -2) and (6, 5.7).
First, let's find the slope of the line passing through these two points. The slope (m) is calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the values (-5, -2) and (6, 5.7) into the formula:
m = (5.7 - (-2)) / (6 - (-5))
m = 7.7 / 11
m = 0.7
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is:
y - y1 = m(x - x1)
Using the point (-5, -2) and the slope m = 0.7, we get:
y - (-2) = 0.7(x - (-5))
y + 2 = 0.7(x + 5)
Simplifying and rearranging:
y + 2 = 0.7x + 3.5
y = 0.7x + 1.5
Therefore, the equation for the function g(x) is: g(x) = 0.7x + 1.5
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There are many possible functions.
However, the only straight line through both points is the one with slope (5.7+2)/(6+5) = 7.7/11 = 77/110
Using the point-slope form, that gives you an equation of
y+2 = 77/110 (x+5)