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satela [25.4K]
3 years ago
8

Y is six more than x divided by three turn it into an expression (y=mx+b format)

Mathematics
1 answer:
Snowcat [4.5K]3 years ago
4 0

We always start from right side in order of operation in any equation

we can set up equation as

step-1:

x divided by three

we can write as

=\frac{x}{3}

step-2:

six more than x divided by three

so, we get

=\frac{x}{3}+6

step-3:

y is six more than x divided by three

so, we get

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

and this is in y=mx+b form

so, we have

y=\frac{x}{3}+6...............Answer


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Y=-x^2+6x-4<br> Find the Axis of Symmetry and the Vertex, Also solve the whole equation.
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Answer:

1. <em>Axis of symmetry</em>: x = 3

2. <em>Vertex:</em> (3,5)

3. <em>Solution of the equation</em>:

<u />

  • x-intercepts:

               (3-\sqrt{5},0) \\\\(3+\sqrt{5},0)

  • y-intercept: (0, -4)

Explanation:

<u>1. Equation:</u>

    y=-x^2+6x-4

<u>2. </u><em><u>Axis of symmetry:</u></em>

That is the equation of a parabola, whose standard form is:

                 y=ax^2+bx+c

Where:    

                 a=-1;b=6;c=-4

The axis of symmetry is the vertical line with equation:

               x=-b/2a

Substitute  a=-1,\text{ and }b=6

          x=-6/[(2)(-1)]=-6/(-2)=3

Thus, the axis of symmetry is:

            x=3

<em><u>3. Vertex</u></em>

<em><u /></em>

The x-coordinate of the vertex is equal to the axys of symmetry, i.e x = 3.

To find the y-xoordinate, substitute this value of x into the equation for y:

               y=-x^2+6x-4\\\\y=-(3)^2+6(3)-4=-9+18-4=5

Therefore, the vertex is (3, 5)

<u>4. Find the x-intercepts</u>

The x-intercepts are the roots of the equation, which are the points wher y = 0.

        y=-x^2+6x-4=0

Use the quadratic equation:

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<u>5. Find the y-intercept</u>

<u />

The y-intercet is the value of y when x=0:

         y=-x^2+6x-4\\\\y=-(0)^2+6(0)-4=-4

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