How do you find the x and y intercept of $3 x - y = 5$ $3x − y = 5$ ?

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Answer 1 · 2016-07-07T16:30:45

$x_{intercept} = \frac{5}{3}$ $x_("intercept")=5/3$

$y_{intercept} = - 5$ $y_("intercept")=-5$

$Determine y_{intercept}$ $color(blue)("Determine "y_("intercept"))$

The y-axis crosses the x-axis at $x = 0$ $x=0$ so to find the y-intercept substitute $x = 0$ $x=0$ into the equation

$3 x - y = 5 \to 3 (0) - y = 5$ $color(brown)(3x-y=5)color(blue)(" "->" "3(0)-y=5$

But $3 \times 0 = 0$ $3xx0=0$ giving

$- y = 5$ $-y=5$

Multiply both sides by $(- 1)$ $(-1)$

$(- y) \times (- 1) = 5 \times (- 1)$ $(-y)xx(-1)=5xx(-1)$

$y = - 5$ $y=-5$
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$Determine x_{intercept}$ $color(blue)("Determine "x_("intercept"))$

The x-axis crosses the y-axis at $y = 0$ $y=0$ so to find the x-intercept substitute $y = 0$ $y=0$ into the equation

$3 x - y = 5 \to 3 x - 0 = 5$ $color(brown)(3x-y=5)color(blue)(" "->" "3x-0=5$

$3 x = 5$ $color(brown)(3x=5)$

Divide both sides by $3$ $color(blue)(3)$

$\frac{3}{3} \times x = \frac{5}{3}$ $color(brown)(3/(color(blue)(3)) xx x=5/(color(blue)(3))$

But $\frac{3}{3} = 1$ $3/3=1$

$x = \frac{5}{3}$ $x=5/3$

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$3 x - y = 5 \to y = 3 x - 5$ $color(brown)(3x-y=5)" "->" "color(blue)(y=3x-5)$
Tony B

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