Question

How do you write the standard form of a line given x-intercep t= 3, y-intercept = 2 ?

Answer 1

The standard form of line is in the form of $Ax + By = C$ Where A is a positive integer, and B and C are integers. The standard form of a line is just another way of writing the equation of line. The x – intercept is where a line crosses the x-axis, and y-intercept is the point where the line crosses the y- axis. Here with standard form of line equation and then with slope formula we solve this with basic mathematical calculation and complete step by step explanation
Formula used:
Two points slope formula
$m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$

Complete step by step answer: The equation of a line is in standard form $Ax + By = C$
Slope intercept form is $y = mx + c$ , Where m is the slope and b the y-intercept.
To calculate m use the gradient formula mentioned in formula used, we get $m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$
Now with given x – intercept and y – intercept, we get two points (3,0) and (0,2)
Let $({x_1},{y_1}) = (3,0)$ and $({x_2},{y_2}) = (0,2)$
Now apply this points in gradient formula, we get
$\Rightarrow m = \dfrac{{2 - 0}}{{0 - 3}} = - \dfrac{2}{3}$
Now substitute m value and b intercept in the slope intercept form, we get
$\Rightarrow y = - \dfrac{2}{3}x + 2$
Multiply through by 3, we get
$\Rightarrow 3y = - 2x + 6$
Arrange in the standard form of straight line
$\Rightarrow 2x + 3y = 6$
Hence, the standard form of a line given x-intercept= 3, y-intercept = 2 is $2x + 3y = 6$

Note:
The intercepts are given two points with which we find slope and then with slope – intercept form which is also known as gradient formula. To determine the x-intercepts, we set y equal to zero and solve x, similarly, to determine the y-intercept, we set x equal to zero and solve for y. The slope of a line characterized the direction of a line. To find slope you divide the difference of the y-coordinate of 2 points on a line by the difference of x-coordinates of those same 2 points.