Question

1. slope - intercept form

(y = mx + b)
(y - 0 = -\frac{2}{3}(x - 6))
(y = -\frac{2}{3}x + 4)

6/10
what is the general form of the slope - intercept equation?
options:
(y = \frac{a}{x}+b)
(ax + by = c)
(y = mx + b)
(y = ax^{2}+bx + c)

Explanation:

Step1: Recall Slope-Intercept Form

The slope - intercept form of a linear equation is a fundamental concept in algebra (a subfield of mathematics) that represents a linear relationship between \(x\) and \(y\). The general form of the slope - intercept equation is \(y = mx + b\), where \(m\) is the slope of the line and \(b\) is the \(y\) - intercept (the value of \(y\) when \(x = 0\)).

Looking at the options:

• Option 1: \(y=\frac{a}{x}+b\) is not a linear equation (it is a rational function), so it cannot be the slope - intercept form of a linear equation.
• Option 2: \(ax + by=c\) is the standard form of a linear equation, not the slope - intercept form.
• Option 3: \(y = ax^{2}+bx + c\) is the general form of a quadratic equation (a second - degree polynomial equation), not a linear equation, so it is not the slope - intercept form.
• Option 4: \(y=mx + b\) (where \(m\) can be represented as any coefficient, including \(a\) in a more general notation - but the structure \(y=\text{(slope)}x+\text{(y - intercept)}\) is captured by \(y = mx + b\)) is the correct slope - intercept form.

Answer:

The option with \(y = mx + b\) (the bottom - right option among the four given options)