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.(1 point)
Responses
b=−5
b equals negative 5
b=12.29
, b equals 12.29
b=15.71
b equals 15.71
b=11
b=15.71
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 5 to 5 in increments of 1. An upward slanting line is plotted on the coordinate plane. The upward slanting line with arrows at both ends passes through the following closed points: left parenthesis negative 4 comma start fraction negative 10 over 3 end fraction right parenthesis, and left parenthesis negative 1 comma start fraction negative 4 over 3 end fraction right parenthesis.
Determine the initial value and the rate of change of the linear function as given in the graph.
(1 point)
Responses
The initial value is −2, and the rate of change is 2/3.
The initial value is , negative 2, , and the rate of change is , Start Fraction 2 over 3 End Fraction, .
The initial value is −2/3, and the rate of change is 2/3.
The initial value is , negative Start Fraction 2 over 3 End Fraction, , and the rate of change is , Start Fraction 2 over 3 End Fraction, .
The initial value is 2/3, and the rate of change is −2/3.
The initial value is , Start Fraction 2 over 3 End Fraction, , and the rate of change is , negative Start Fraction 2 over 3 End Fraction, .
The initial value is 1/6, and the rate of change is 3/2.
The initial value is , Start Fraction 1 over 6 End Fraction, , and the rate of change is , Start Fraction 3 over 2 End Fraction, .
The initial value is −2/3, and the rate of change is 2/3.
Good morning
Good morning! How can I assist you today?
hi
To find the initial value or y-intercept (b) of the linear function given the rate of change (m) and a point (x, y), we can use the point-slope form of a linear equation.
The point-slope form of a linear equation is: y - y1 = m(x - x1), where (x1, y1) is the given point.
In this case, the rate of change (m) is -4/7 and the point (14, 3) is given. Plugging in these values into the point-slope form, we get:
3 - y1 = (-4/7)(14 - x1)
Next, to solve for b (the y-intercept), we can substitute the values of x and y from the given point (14, 3) into the equation:
3 - y1 = (-4/7)(14 - 14)
Simplifying the equation gives:
3 - y1 = 0
Adding y1 to both sides of the equation, we get:
3 = y1
Therefore, the initial value or y-intercept (b) is equal to 3.