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]
