Mathematics, 23.07.2019 05:40, CalCDanG

Hello! it would be much appreciated if someone could show me the steps of how to change from standard form to y intercept form and also explain how i can determine the slope and y intercept in the 2nd question

Hello! it would be much appreciated if someone could show me the steps of how to change from standa

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answered: alexsince4835

Standard Form:

Ax + By = C

y-intercept Form:

y = mx + b

Changing from Standard to y-intercept:

When you are given an equation in standard form, you are provided with the coefficients for the x and y variables, along with a constant. The first thing we should do is isolate the y variable, as y-intercept form has only a y variable on one side. This can be done like so (using part A as an example):

5x - y + 3 = 0 (Original equation)

-y = -5x - 3 Subtract 3 and 5x from both sides.

y = 5x + 3 Divide both sides by the coefficient of the y variable.

As you can see, the equation now is in y-intercept form.

Determining the Slope and y-intercept:

For your case, the easiest (and intended) way of finding the slope and y-intercept is to convert the 2 given equations into y-intercept form. Do the same thing we did previously:

a.) x + 2y - 6 = 0

2y = -x + 6

y = - $\frac{1}{2}$ x + 3

b.) 3x - 2y + 12 = 0

-2y = -3x - 12

y = $\frac{3}{2}$ x + 6

From here, it's just a matter of extracting the information from the 2 equations. Recall that y-intercept form is

y = mx + b

where b is the y-intercept

and m is the slope.

In the first equation, the m = - $\frac{1}{2}$ , meaning - $\frac{1}{2}$ is the slope, and b = 3, meaning the y-intercept is 3.

In the second equation, the m = $\frac{3}{2}$ , meaning $\frac{3}{2}$ is the slope, and b = 6, meaning the y-intercept is 6.

Hope this helps! :)

answered: Guest

b. the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

f(-2) = -3f(1) = 6 . . . estimated from f(x) = (x+2)^2-3, which matches points on the graph (-1,-2) and (0, 1)

so the change in y-value for function f is (6 )) = 9.

the table tells us

g(-2) = 1g(1) = 31

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

answered: Guest

The correct answer will be d. -4

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Hello! it would be much appreciated if someone could show me the steps of how to change from standa...