Carson M. answered • 03/29/20

Dedicated, Experienced, and Success-Driven Academic Tutor

The equation of the line with an __x-intercept__ of **2** and a __y-intercept__ of **4** can be written in the form **y = mx + b**

- At any
__x-intercept__in the coordinate plane, the corresponding__y-value__is**0** - It can be said the line has an
__x-intercept__at the point**(2, 0)** - At any y
__-intercept__in the coordinate plane, the corresponding__x-value__is**0** - It can be said the line has an y
__-intercept__at the point**(0, 4)** - Knowing
*two*distinct points in a given line enables us to calculate the__slope__of the line - Recall the
__Slope Formula___{2}**- y**_{1}**) / (x**_{2}**- x**_{1}**)** **m = (4 - 0) / (0 - 2)****m = 4 / (-2)**__m = -2__- Substituting this into
__Slope-Intercept Form__yields**y = -2x + b** - By definition of "slope-intercept," the value of
**b**is equal to the__y-coordinate__of the__y-intercept__, so it can be determined that the resulting linear equation is**y = -2x + 4** - However if you don't know the
__y-intercept__(unlike this particular case), the linear equation can be proven by substituting a coordinate pair along the line into the equation to solve for**b**as follows: **y = -2x + b****(4) = -2(0) + b**__b = 4__- or
**(0) = -2(2) + b**__b = 4__- Therefore, the equation of the line with an
__x-intercept__of**2**and a__y-intercept__of**4**can be written in the form**y = -2x + 4**or**y = 4 - 2x**where**m = -2**and**b = 4**