### Video Transcript

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.