Question: What is the equation of the line in standard form?
The standard form for a line is :
y = mx + b
where m is the slope and b is the intercept with y axis.
First, we are going to find the slope, choosing any two points on the line. For example (X1, Y1) = (-4,0) and (X2, Y2) = (0,3). Then, by definition the slope is:
[tex]m\text{ = }\frac{Y2\text{ - Y1}}{X2\text{ - X1}}\text{ = }\frac{3-0}{0-(-4)}\text{ = }\frac{3}{0+\text{ 4}}\text{ = }\frac{3}{4}[/tex]
so, our new line equation would be:
[tex]y\text{ = mx + b = }\frac{3}{4}x\text{ + b}[/tex]
that is:
[tex]y\text{ = }\frac{3}{4}x\text{ + b}[/tex]
Now, we are going to find the y-intercept. This is also accomplished by picking two points on the line and solving for b. For example (X2, Y2) = (0,3). So, for above equation we have:
[tex]3\text{ = }\frac{3}{4}(0)\text{ + b}[/tex]
then
[tex]3\text{ = 0 + b = b}[/tex]
Then, we have b = 3.
Now, replacing the values of the slope and the intercept previously found, we obtain the equation of the line :
[tex]y\text{ = mx + b = }\frac{3}{4}x\text{ + }3[/tex]
that is
[tex]y\text{ = }\frac{3}{4}x\text{ + }3[/tex]
