Question
Find the initial value of the linear function given that the rate of change is M = -4/7 and (14,3) is an (x,y) value of the linear function
Answers
GPT 3.5
The initial value of the linear function, or the y-intercept, can be found by using the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope.
In this case, we have the point (14,3) and the slope M = -4/7. Plugging in these values into the equation, we have:
3 - y1 = (-4/7)(14 - x1)
Next, we can rearrange the equation to solve for y1:
3 - y1 = (-4/7)(14 - x1)
3 - y1 = (-4/7)(14) + (-4/7)(-x1)
3 - y1 = -8 + (4/7)x1
-y1 = -8 + (4/7)x1 - 3
-y1 = -11 + (4/7)x1
Therefore, the initial value of the linear function is -11.
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope.
In this case, we have the point (14,3) and the slope M = -4/7. Plugging in these values into the equation, we have:
3 - y1 = (-4/7)(14 - x1)
Next, we can rearrange the equation to solve for y1:
3 - y1 = (-4/7)(14 - x1)
3 - y1 = (-4/7)(14) + (-4/7)(-x1)
3 - y1 = -8 + (4/7)x1
-y1 = -8 + (4/7)x1 - 3
-y1 = -11 + (4/7)x1
Therefore, the initial value of the linear function is -11.