Assignment: Converting Between Forms Convert each equation of a line to the requ

Question

Assignment: Converting Between Forms

Convert each equation of a line to the requested form.

Part I: Practice Converting Equations to Different Forms 1. Write the equation y=1/2x+3 in standard form.


2. Write the equation 9x+2y=6 in slope-intercept form.

3. Write the equation y-3=4(x+1)in standard form.


4. Write the equation y+7=-2(x-3) in slope-intercept form.


5. The equation y-5=3(x-2) is written in point-slope form. Write this equation in the following ways:

a. slope-intercept form

b. standard form


Part II: Create Your Own Conversion Problem Now it’s time for you to create your own problem that involves converting three different equations of lines to different forms. First, write three (3) equations of lines in the following forms: a) point-slope form, b) slope-intercept form, and c) standard form. Next, choose another form to write each equation in, and then show all the steps required to convert each equation to the other form.

Explanation / Answer

1. Write the equation y=1/2x+3 in standard form.
Ans: y=1/2x+3 => 2y=x+6 => x-2y=-6 (ax+by=c is the standard form)

2. Write the equation 9x+2y=6 in slope-intercept form.
Ans: y=mx+b is the slope intercept form.
        9x+2y=6 => 2y=-9x+6 => y=(-9/2)x+3
        y=(-9/2)x+3 is in the slope intercept form.

3. Write the equation y-3=4(x+1)in standard form.
Ans: y-3=4(x+1) => y-3=4x+4 => 4x-y=-7
        4x-y=-7 is in the standard form.

4. Write the equation y+7=-2(x-3) in slope-intercept form.
Ans: y=mx+b is the slope intercept form.
        y+7=-2(x-3) => y=-2x+6-7 => y=-2x-1
        y=-2x-1 is the slope intercept form of the given equation.

5. The equation y-5=3(x-2) is written in point-slope form. Write this equation in the following ways:
a. slope-intercept form
b. standard form
a) Slope intercept form:
    y=3x-1 is the slope intercept form of the equation.
b) Standard Form:
    3x-y=1 is the standard form.
   

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