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Lesson 11: Converting Standard Form to Slope-Intercept Form

Order the steps to correctly change the equation from Standard Form to Slope-Intercept Form.

START: STANDARD FORM

[tex]\[
-4x + 3y = 3
\][/tex]

1. Add [tex]\(4x\)[/tex] to both sides:
[tex]\[
3y = 4x + 3
\][/tex]

2. Divide both sides by 3:
[tex]\[
y = \frac{4}{3}x + 1
\][/tex]

END: SLOPE-INTERCEPT FORM

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After you have correctly ordered the steps, use the slope-intercept form equation to answer these questions:

The slope is:
[tex]\[
\square
\][/tex]

The [tex]\(y\)[/tex]-intercept is:
[tex]\[
\square
\][/tex]

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Answer :

GinnyAnswer
To convert the given equation from Standard Form to Slope-Intercept Form, we will follow these steps:

1. Start with the equation in Standard Form:
[tex]\[ -4x + 3y = 3 \][/tex]

2. Add [tex]\( 4x \)[/tex] to both sides to start isolating [tex]\( y \)[/tex]:
[tex]\[ 3y = 4x + 3 \][/tex]

3. Divide both sides by 3 to solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{4}{3}x + 1 \][/tex]

Now we have the equation in Slope-Intercept Form ([tex]\( y = mx + b \)[/tex]), where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.

To answer the questions:

The slope ([tex]\( m \)[/tex]) is:
[tex]\[ \boxed{\frac{4}{3}} \][/tex]

The y-intercept ([tex]\( b \)[/tex]) is:
[tex]\[ \boxed{1} \][/tex]

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