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Write the equation of the line π¦ = β2π₯ + 6 in the two-intercept form.

Write the equation of the line π¦ equals negative two π₯ plus six in the two-intercept form.

We recall first that the two-intercept form of the equation of a straight line, which intercepts the π₯-axis at π, zero and intercepts the π¦-axis at zero, π, is π₯ over π plus π¦ over π is equal to one. We therefore need to take the equation weβve been given and rearrange it. We begin by adding two π₯ to each side of the equation, which gives two π₯ plus π¦ is equal to six. Weβve now collected the π₯- and π¦-terms on one side of the equation, with the constant term on the other. But this equation isnβt in two-intercept form because the constant term on the right-hand side must be equal to one. We therefore need to divide both sides of the equation by six. Doing so gives two π₯ over six plus π¦ over six is equal to one.

We can then simplify the first quotient by canceling a factor of two in both the numerator and denominator to give π₯ over three plus π¦ over six equals one. And this equation is now in the two-intercept form. Although we havenβt specifically been asked to do this, we can use this form to determine the π₯- and π¦-intercepts of this straight line. The value of π is three, and the value of π is six.

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