Question 158993
knowing the x-intercept and the y-intercept give you 2 point from which you can calculate the slope.
in your example, y-intercept = 2 means the point is (0,2) since the y-intercept is the y value when x value = 0.
x-intercept = 3 means the point is (3,0) since the x-intercept is the x value when y = 0.
now that you have 2 points, you can calculate the slope.
slope-intercept formula is y = m*x + b where m is the slope and b is the y-intercept.
your 2 data points are (x1,y1), and x2,y2) from which you can calculate the slope by using the following equation
{{{slope = (y2-y2)/(x2-x1)}}}
let (x2,y2) = (0,2)
let (x1,y1) = (3,0)
slope = {{{(2-0)/(0-3)}}} = {{{2/-3}}} = {{{-(2/3)}}}
slope-intercept equation now becomes {{{y=-(2/3)*x + b}}}
now all you have to do is solve for b.
to solve for b, use one of the points that are part of the line.
we'll use (3,0) first.
{{{y = -(2/3)*x + b}}} becomes {{{0 = -(2/3)*3 + b}}}
this becomes {{{0 = -2 + b}}}
solving for b gets
b = 2
full slope-intercept equation then looks like {{{y=-(2/3)*x+2}}}
using this formula and substituting for values using the other point of (0,2) gets {{{2 = -(2/3)*(0) + 2}}} which becomes 2 = 2 which is an identity proving the formula is correct.
using this formula and substituting for values using the first point used of (3,0) gets {{{0 = -(2/3)*3 + 2}}} which becomes {{{0 = -2*x + 2}}} which becomes 0 = 0 which is an identify proving the formula is correct.
the answer is {{{y=-(2/3)*x+2}}}