The standard form of a line is just another way of writing the equation of a line. It gives all of the same information as the slope-intercept form. The slope-intercept form of a line is: y = mx + b. We are expected to rewrite it in the form Ax + By = C. which is the standard equation of the line.
Step 1:
We get the equation of the line.
Given the x-intercept and the y-intercept, they can be adjusted to give the following points.
(0,5) gotten from the y-intercept and (3,0) gotten from the x-intercept
STEP 2
Insert the points into the formula.
[tex]\begin{gathered} \text{Equation of a line gives} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ \text{also, m=}\frac{\text{y-y}_1}{x-x_1} \\ \text{Equating the above equations for the slope, we have} \\ \frac{y_2-y_1}{x_2-x_1}=\frac{\text{y-y}_1}{x-x_1} \\ \frac{0-5}{3-0}=\frac{y-5}{x-0} \\ -\frac{5}{3}=\frac{y-5}{x} \\ Cross\text{ multiply.} \\ -5x=3(y-5) \\ -5x=3y-15 \\ \operatorname{Re}arrange\text{ the equation} \\ 5x+3y=15 \\ \end{gathered}[/tex]Therefore, the standard equation of the line is 5x+3y=15 which is similar to Ax+By=C as stated above.
