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Math Chapter 7 : Topic 9
General Line Equation
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A linear equation in two variables represents:
Reasoning: All first-degree equations in $x$ and $y$ form a straight line.$Ax+By+C=0$
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Which condition must hold for a linear equation?
Reasoning: Linear means first-degree equation. $⟹$ $Ax+By+C=0$
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The general form of a straight line is:
Reasoning: Standard general linear form. $⟹$ $Ax+By+C=0$
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Equation $2x+3y-6=0$ represents:
Reasoning: It is linear in $x$ and $y$. $⟹$ $Ax+By+C=0$
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A linear equation always contains:
Reasoning: Both variables are first degree. $⟹$ $Ax+By+C=0$
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To convert general form to slope-intercept form, we:
Reasoning: Rearranging gives $y=mx+c$.
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Equation $Ax+By+C=0$ becomes slope-intercept form by:
Reasoning: Solve for $y$.Slope-intercept form $y=mx+c$.
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Which form is obtained after rearranging general form?
Reasoning: Algebraic rearrangement gives Slope-intercept form $y=mx+c$.
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A linear equation graph is always:
Reasoning: First-degree equation gives line. $⟹$ $Ax+By+C=0$
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Which equation is NOT linear?
Reasoning: Contains $x^{2}$, not linear.
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Slope of line from $Ax+By+C=0$ is:
Reasoning: Rearranging gives slope. Slope-intercept form $y=mx+c$.
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Why does a linear equation represent a straight line?
Reasoning: First-degree equations produce straight lines.
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Which transformation gives intercept form?
Reasoning: Divide by $x$ and $y$ intercepts. Intercept form $\frac{x}{a}$ $+$ $\frac{y}{b}$ $=1$.
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General form is useful because it:
Reasoning: Any line can be written in this form. $⟹$ $Ax+By+C=0$
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If $B=0$ in $Ax+By+C=0$, the line is:
Reasoning: Equation becomes $x=$ constant.
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If $A=0$, the line becomes:
Reasoning: Equation becomes $y=$ constant.
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A straight line equation always has:
Reasoning: Linear means first degree in $x$ and $y$. $⟹$ $Ax+By+C=0$
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Which step converts general form to intercept form?
Reasoning: Normalize equation. Intercept form $\frac{x}{a}$ $+$ $\frac{y}{b}$ $=1$.
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Graph of $3x+2y-6=0$ is:
Reasoning: Linear equation.
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Which property confirms linearity?
Reasoning: Straight line has constant slope.
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General form cannot represent:
Reasoning: It is strictly linear.
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If equation is linear, graph has:
Reasoning: Straight line has no curvature.
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Which is equivalent form of $Ax+By+C=0$?
Reasoning: Can be converted into all standard forms.
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A line passes through origin if:
Reasoning: $Ax+By=0$
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The most general representation of a straight line is:
Reasoning: All are equivalent forms of a line.
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