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  1. Asked: January 22, 2021In:

    write the equation of a line if the gradient is 1 and the y intercept is \dfrac{1}{5}

    Sengemegz
    Sengemegz Moderator

    Equation of a line: $y=mx+c$ Gradient(m)=$1$ and Intercept(c)=$\dfrac{1}{5}$ $\Rightarrow y=x+\dfrac{1}{5}$

    Equation of a line: y=mx+c
    Gradient(m)=1 and Intercept(c)=\dfrac{1}{5}
    \Rightarrow y=x+\dfrac{1}{5}

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  2. Asked: January 22, 2021In:

    State the gradient and the y intercept of x+y=4

    Sengemegz
    Sengemegz Moderator

    $x+y=4$ $\Rightarrow y=-x+4$ $\therefore$ Gradient=$-1$ and y-intercept=$4$

    x+y=4
    \Rightarrow y=-x+4
    \therefore Gradient=-1 and y-intercept=4

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  3. Asked: January 22, 2021In:

    State the gradient and the y intercept of y+2x=3

    Sengemegz
    Sengemegz Moderator

    $y+2x=3$ $\Rightarrow y=-2x+3$ $\therefore$ Gradient=$-2$ and y-intercept=$3$

    y+2x=3
    \Rightarrow y=-2x+3
    \therefore Gradient=-2 and y-intercept=3

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  4. Asked: January 22, 2021In:

    State the gradient and the y intercept of 2y-x=3

    Sengemegz
    Sengemegz Moderator
    This answer was edited.

    $2y-x=3$ $\Rightarrow 2y=x+3$ Divide both sides by 2 $\Rightarrow \dfrac{2}{2}y=\dfrac{1}{2}+\dfrac{3}{2}$ $\Rightarrow y=\dfrac{1}{2}+\dfrac{3}{2}$ $\therefore$ Gradient=$\dfrac{1}{2}$ and y-intercept=$\dfrac{3}{2}$

    2y-x=3
    \Rightarrow 2y=x+3
    Divide both sides by 2
    \Rightarrow \dfrac{2}{2}y=\dfrac{1}{2}+\dfrac{3}{2}
    \Rightarrow y=\dfrac{1}{2}+\dfrac{3}{2}
    \therefore Gradient=\dfrac{1}{2} and y-intercept=\dfrac{3}{2}

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  5. Asked: January 22, 2021In:

    State the gradient and the y intercept of x+3y=6

    Sengemegz
    Sengemegz Moderator

    $x+3y=6$ $\Rightarrow 3y=-x+6$ Divide both sides by 3 $\Rightarrow \dfrac{3}{3}y=-\dfrac{1}{3}+\dfrac{6}{3}$ $\Rightarrow y=-\dfrac{1}{3}+2$ $\therefore$ Gradient=$-\dfrac{1}{3}$ and y-intercept=$2$

    x+3y=6
    \Rightarrow 3y=-x+6
    Divide both sides by 3
    \Rightarrow \dfrac{3}{3}y=-\dfrac{1}{3}+\dfrac{6}{3}
    \Rightarrow y=-\dfrac{1}{3}+2
    \therefore Gradient=-\dfrac{1}{3} and y-intercept=2

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  6. Asked: January 22, 2021In:

    State the gradient and the y intercept of 2x-y=5

    Sengemegz
    Sengemegz Moderator

    $2x-y=5$ $\Rightarrow y=2x-5$ $\therefore$ Gradient=$2$ and y-intercept=$-5$

    2x-y=5
    \Rightarrow y=2x-5
    \therefore Gradient=2 and y-intercept=-5

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  7. Asked: January 22, 2021In:

    State the gradient and the y intercept of x+2y+4=0

    Sengemegz
    Sengemegz Moderator

    $x+2y+4=0$ $\Rightarrow 2y=-x-4$ Divide both sides by 2 $\Rightarrow \dfrac{2}{2}y=-\dfrac{1}{2}-\dfrac{4}{2}$ $\Rightarrow y=-\dfrac{1}{2}-2$ $\therefore$ Gradient=$-\dfrac{1}{2}$ and y-intercept=$-2$

    x+2y+4=0
    \Rightarrow 2y=-x-4
    Divide both sides by 2
    \Rightarrow \dfrac{2}{2}y=-\dfrac{1}{2}-\dfrac{4}{2}
    \Rightarrow y=-\dfrac{1}{2}-2
    \therefore Gradient=-\dfrac{1}{2} and y-intercept=-2

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  8. Asked: January 22, 2021In:

    State the gradient and the y intercept of 2x=y-1

    Sengemegz
    Sengemegz Moderator

    $2x=y-1$ $\Rightarrow y=2x+1$ $\therefore$ Gradient=$2$ and y-intercept=$1$

    2x=y-1
    \Rightarrow y=2x+1
    \therefore Gradient=2 and y-intercept=1

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  9. Asked: January 22, 2021In:

    State the gradient and the y intercept of 3y=x-1

    Sengemegz
    Sengemegz Moderator

    $3y=x-1$ Divide both sides by $3$ $\Rightarrow \dfrac{3}{3}y=\dfrac{1}{3}x-\dfrac{1}{3}$ $\Rightarrow y=\dfrac{1}{3}x-\dfrac{1}{3}$ $\therefore$ Gradient=$\dfrac{1}{3}$ and y-intercept=$-\dfrac{1}{3}$

    3y=x-1
    Divide both sides by 3
    \Rightarrow \dfrac{3}{3}y=\dfrac{1}{3}x-\dfrac{1}{3}
    \Rightarrow y=\dfrac{1}{3}x-\dfrac{1}{3}
    \therefore Gradient=\dfrac{1}{3} and y-intercept=-\dfrac{1}{3}

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  10. Asked: January 22, 2021In:

    State the gradient and the y intercept of \sqrt{3y}-x=6

    Sengemegz
    Sengemegz Moderator

    $\sqrt{3}y-x=6$ $\Rightarrow \sqrt{3}y=x+6$ Divide both sides by $\sqrt{3}$ $\Rightarrow \dfrac{\sqrt{3}}{\sqrt{3}}y=\dfrac{1}{\sqrt{3}}x+\dfrac{6}{\sqrt{3}}$ $\Rightarrow y=\dfrac{1}{\sqrt{3}}x+\dfrac{6}{\sqrt{3}}$ Rationalize the denominator $\Rightarrow y=\dfrac{\sqrt{3}}{3}x+\dfrac{6\sqrt{3}}{3}Read more

    \sqrt{3}y-x=6
    \Rightarrow \sqrt{3}y=x+6
    Divide both sides by \sqrt{3}
    \Rightarrow \dfrac{\sqrt{3}}{\sqrt{3}}y=\dfrac{1}{\sqrt{3}}x+\dfrac{6}{\sqrt{3}}
    \Rightarrow y=\dfrac{1}{\sqrt{3}}x+\dfrac{6}{\sqrt{3}}
    Rationalize the denominator
    \Rightarrow y=\dfrac{\sqrt{3}}{3}x+\dfrac{6\sqrt{3}}{3}
    \Rightarrow y=\dfrac{\sqrt{3}}{3}x+2\sqrt{3}
    \therefore Gradient=\dfrac{\sqrt{3}}{3} and y-intercept=2\sqrt{3}

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