Question:
Solution:
Let the following linear function:
[tex]4x\text{ + 5y = 20}[/tex]
solve for 5y:
[tex]5y\text{ = }20-4x[/tex]
solving for y, we get:
[tex]y\text{ = }-\frac{4}{5}x\text{ + }4[/tex]
the y- intercept is when x = 0, then replacing x = 0 into previous equation we get:
[tex]y\text{ = }-\frac{4}{5}(0)\text{ + }4\text{ = 4}[/tex]
then the y-intercept is the point:
(x,y) = (0,4)
Now, the x-intercept is when y = 0, the replacing y = 0 into the equation:
[tex]y\text{ = }-\frac{4}{5}x\text{ + }4[/tex]
we get:
[tex]0\text{ = }-\frac{4}{5}x\text{ + }4[/tex]
this is equivalent to:
[tex]-4\text{= }-\frac{4}{5}x\text{ }[/tex]
this is equivalent to:
[tex]4\text{= }\frac{4}{5}x\text{ }[/tex]
solving for x, we get:
[tex]x\text{ = }\frac{20}{4}\text{ = 5}[/tex]
then the x-intercept is the point:
(x,y) = (5,0)
Then, we can conclude that the correct answer is:
1. the y-intercept is the point (x,y) = (0,4).
2. the x-intercept is the point (x,y) = (5,0).
and the graph of the line is:
