Write the equation of the line 𝑦
equals negative two 𝑥 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 𝑥-axis
at 𝑎, zero and intercepts the 𝑦-axis at zero, 𝑏, is 𝑥 over 𝑎 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 𝑥 to each
side of the equation, which gives two 𝑥 plus 𝑦 is equal to six. We’ve now collected the 𝑥- 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 𝑥 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
𝑥 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 𝑥- and 𝑦-intercepts
of this straight line. The value of 𝑎 is three, and the
value of 𝑏 is six.