Question Video: Finding the Equation of a Straight Line

Write the equation of the line 𝑦 = βˆ’2π‘₯ + 6 in the two-intercept form.

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Video Transcript

Write the equation of the line 𝑦 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‘Ž, zero and intercepts the 𝑦-axis at zero, 𝑏, is π‘₯ over π‘Ž plus 𝑦 over 𝑏 is equal to one. We therefore need to take the equation we’ve been given and rearrange it. We begin by adding two π‘₯ to each side of the equation, which gives two π‘₯ plus 𝑦 is equal to six. We’ve now collected the π‘₯- and 𝑦-terms on one side of the equation, with the constant term on the other. But this equation isn’t 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 𝑦 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 𝑦 over six equals one. And this equation is now in the two-intercept form. Although we haven’t specifically been asked to do this, we can use this form to determine the π‘₯- and 𝑦-intercepts of this straight line. The value of π‘Ž is three, and the value of 𝑏 is six.

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