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Question Number 32792 by Rio Mike last updated on 02/Apr/18

the equation   3x− 5=15 represents a straight line.  a) find one point on this line.  b)find the coordinates of the points when  the line cuts the x−axis and the y−axis  c)find the gradient of this line.

$${the}\:{equation}\: \\ $$$$\mathrm{3}{x}−\:\mathrm{5}=\mathrm{15}\:{represents}\:{a}\:{straight}\:{line}. \\ $$$$\left.{a}\right)\:{find}\:{one}\:{point}\:{on}\:{this}\:{line}. \\ $$$$\left.{b}\right){find}\:{the}\:{coordinates}\:{of}\:{the}\:{points}\:{when} \\ $$$${the}\:{line}\:{cuts}\:{the}\:{x}−{axis}\:{and}\:{the}\:{y}−{axis} \\ $$$$\left.{c}\right){find}\:{the}\:{gradient}\:{of}\:{this}\:{line}. \\ $$$$ \\ $$

Commented by Joel578 last updated on 02/Apr/18

Did you mean 3x − 5 = 15 + y  or really 3x − 5 = 15?

$$\mathrm{Did}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{3}{x}\:−\:\mathrm{5}\:=\:\mathrm{15}\:+\:{y}\:\:\mathrm{or}\:\mathrm{really}\:\mathrm{3}{x}\:−\:\mathrm{5}\:=\:\mathrm{15}? \\ $$

Commented by Rio Mike last updated on 02/Apr/18

i mean   3x −  5y = 15

$${i}\:{mean}\:\:\:\mathrm{3}{x}\:−\:\:\mathrm{5}{y}\:=\:\mathrm{15} \\ $$

Answered by Joel578 last updated on 03/Apr/18

3x − 5y = 15  y = (3/5)x − 3    (a) x = 10 → y = 3  (b) Intersect with x−axis  → y = 0 → x = 5  (5,0)         With y−axis  →  x = 0 → y = −3  (0,−3)  (c) Gradient = coefficient x = (3/5)

$$\mathrm{3}{x}\:−\:\mathrm{5}{y}\:=\:\mathrm{15} \\ $$$${y}\:=\:\frac{\mathrm{3}}{\mathrm{5}}{x}\:−\:\mathrm{3} \\ $$$$ \\ $$$$\left({a}\right)\:{x}\:=\:\mathrm{10}\:\rightarrow\:{y}\:=\:\mathrm{3} \\ $$$$\left({b}\right)\:\mathrm{Intersect}\:\mathrm{with}\:{x}−\mathrm{axis}\:\:\rightarrow\:{y}\:=\:\mathrm{0}\:\rightarrow\:{x}\:=\:\mathrm{5}\:\:\left(\mathrm{5},\mathrm{0}\right) \\ $$$$\:\:\:\:\:\:\:\mathrm{With}\:{y}−\mathrm{axis}\:\:\rightarrow\:\:{x}\:=\:\mathrm{0}\:\rightarrow\:{y}\:=\:−\mathrm{3}\:\:\left(\mathrm{0},−\mathrm{3}\right) \\ $$$$\left({c}\right)\:\mathrm{Gradient}\:=\:\mathrm{coefficient}\:{x}\:=\:\frac{\mathrm{3}}{\mathrm{5}} \\ $$

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