Question

I need help with this question for math. I would love for some help thank you.

Answer 1

y= -3x+1

Explanation:

Let's start with the y-intercept (initial value). The y-intercept is where the line intersects the y-axis, so the x value should be 0. Here, the y-intercept is (0,1).

The slope is equivalent to the rise over run. We rise three and go to the left 1 which gives us a slope of negative 3 since we went to the left instead of the right.

Equation for a line:

y=mx+b where m is the slope and b is the y-intercept.

We plug in the slope and y-intercept in and get...

y= -3x+1

Answer 2

• slope: -3
• initial value: 1
• equation: y = -3x +1
• partial variation

Explanation:

Slope

To find the slope of the line, it is useful to find two grid intersections that the line passes through. If one of those is on the y-axis, that is a good place to start. Here, that one is (0, 1).

Another can be see up and to the left, at (-1, 4).

The slope formula can be used to find the slope between these points:

m = (y2 -y1)/(x2 -x1)

m = (4 -1)/(-1 -0) = 3/-1 = -3

The slope of the line is -3.

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Initial value:

This is the value that the function has when x=0. It is the y-intercept. We identified that value in the previous section as 1.

The initial value is 1.

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Equation:

The slope-intercept equation of the line is of the form ...

y = mx + b . . . . . . . where m is the slope (-3) and b is the y-intercept (1).

Filling in the values we know, the equation is ...

y = -3x +1

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Variation:

The line represents "direct variation" only if the y-intercept is zero. That is, the equation will be of the form ...

y = kx

with no added constant. The value "k" is called the constant of proportionality, or "rate of change."

You will notice the equation for the line on this graph has a y-intercept of 1, so does not represent direct variation. Of the two answer choices, the appropriate one is ...

Partial Variation