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Convert the equation from Standard Form to Slope-Intercept Form.

[tex]\[
-4x + 3y = -6
\][/tex]

Show your work in the box below.

[tex]\[
\boxed{}
\][/tex]

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

1. The slope is:
[tex]\[
\boxed{}
\][/tex]

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

Sagot :

GinnyAnswer
To convert the equation from standard form to slope-intercept form, follow these steps:

Original equation:
[tex]\[ -4x + 3y = -6 \][/tex]

1. Isolate the term with [tex]\(y\)[/tex] on one side of the equation.

[tex]\[ 3y = 4x - 6 \][/tex]

2. Divide every term by the coefficient of [tex]\(y\)[/tex], which is 3, to solve for [tex]\(y\)[/tex].

[tex]\[ y = \frac{4}{3}x - 2 \][/tex]

So, the slope-intercept form of the equation is:
[tex]\[ y = \frac{4}{3}x - 2 \][/tex]

From this equation, we can identify the slope (m) and the y-intercept (b):

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

- The y-intercept (b) is:
[tex]\[ -2 \][/tex]

Therefore:

- The slope is:
[tex]\[ 1.3333333333333333 \][/tex] or, equivalently, [tex]\[ \frac{4}{3} \][/tex]

- The y-intercept is:
[tex]\[ -2 \][/tex]
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