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Math Chapter 7 : Topic 4
Line Equation (y=mx+c)
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In the equation $y=mx+c$, the value of $m$ represents:
Reasoning: $m$ gives the rate of change of $y$ with respect to $x$.
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In $y=mx+c$, $c$ represents:
Reasoning: $c$ is the value of $y$ when $x=0$.
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Find the equation of line with slope $2$ and $y$-intercept $3$.
Reasoning: Substitute $m=2$, $c=3$ into formula $y=mx+c$.
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Which equation represents a horizontal line?
Reasoning: Slope $=0 ⟹$horizontal line
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Find equation of line with slope $- 1$ and passing through origin.
Reasoning: Intercept is $0 ⟹ y=- x$
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Find equation of line with slope $3$ passing through $(0, - 5)$.
Reasoning: Intercept $=- 5$ ; $y=mx+c$
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Which equation has negative slope?
Reasoning: Coefficient of $x$ is negative ; $y=mx+c$
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The line $y=4x-2$ cuts $y$-axis at:
Reasoning: $y$-intercept $=c=- 2$ ; $y=mx+c$
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Find slope of line $y=- 5x+7$.
Reasoning: Coefficient of $x$ is slope ; $y=mx+c$
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Which equation passes through origin?
Reasoning: $c=0 ⟹$passes origin
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Find equation of line with slope $1$ and passing through $(0,0)$.
Reasoning: $m=1$, $c=0$ ; $y=mx+c$
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If a line is parallel to $x$-axis, its equation is:
Reasoning: Slope $=0 ⟹ y=$ constant ; $y=mx+c$
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Find equation with slope $0$ and intercept $4$.
Reasoning: Both represent same equation ; $y=mx+c$
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Which equation has slope $0$?
Reasoning: No $x$-term$⟹$slope $=0$ ; $y=mx+c$
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Find equation of line with slope $2$ passing through $(0,0)$.
Reasoning: $c=0$ ; $y=mx+c$
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The graph of $y=mx+c$ is always:
Reasoning: Linear equation gives straight line.
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If slope increases, the line becomes:
Reasoning: Larger slope$⟹$steeper line
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Find equation of line with slope $- 2$ and intercept $0$.
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Which equation represents vertical line?
Reasoning: Vertical lines cannot be written in $y=mx+c$ form.
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Equation of line depends on:
Reasoning: Both $m$ and $c$ define the line ; $y=mx+c$
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If $c=0$, the line:
Reasoning: $y=mx$ passes origin ; $y=mx+c$
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Find intercept of line $y=6x-9$.
Reasoning: $c=- 9$ ; $y=mx+c$
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Which equation has slope $1$ and intercept $- 2$?
Reasoning: $m=1$, $c=- 2$ ; $y=mx+c$
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A line with positive slope:
Reasoning: Positive slope increases $y$.
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Which equation has no $y$-intercept?
Reasoning: Vertical line doesn’t cut $y$-axis ; $y=mx+c$
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