Question

1. What is the equation of the line in standard form? A302-10

Answer 1

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:

`m\text{ = }\frac{Y2\text{ - Y1}}{X2\text{ - X1}}\text{ = }(3-0)/(0-(-4))\text{ = }\frac{3}{0+\text{ 4}}\text{ = }(3)/(4)`

so, our new line equation would be:

`y\text{ = mx + b = }(3)/(4)x\text{ + b}`

that is:

`y\text{ = }(3)/(4)x\text{ + b}`

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:

`3\text{ = }(3)/(4)(0)\text{ + b}`

then

`3\text{ = 0 + b = b}`

Then, we have b = 3.

Now, replacing the values of the slope and the intercept previously found, we obtain the equation of the line :

`y\text{ = mx + b = }(3)/(4)x\text{ + }3`

that is

`y\text{ = }(3)/(4)x\text{ + }3`