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Question: How do you write the slope of intercept form of the line \[13x - 11y = - 12\] \[?\]...

How do you write the slope of intercept form of the line 13x−11y=−1213x - 11y = - 12 ??

Explanation

Solution

Hint : The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis or solve the given equation for y gives the required result.

Complete step-by-step answer :
In the equation of a straight line (when the equation is written as “y=mx+b"), the slope is the number “m" that is multiplied on the x, and “b" is the y-intercept (that is, the point where the line crosses the vertical y-axis). This useful form of the line equation is sensibly named the "slope-intercept form".
Consider the given equation of line
⇒13x−11y=−12\Rightarrow 13x - 11y = - 12
As we know the equation of a line in slope-intercept form is y=mx+b.
Rearrange the given equation of line 13x−11y=−1213x - 11y = - 12 in to the slope intercept form.
Subtract 13x from both sides, then
⇒13x−13x−11y=−13x−12\Rightarrow13x - 13x - 11y = - 13x - 12
⇒−11y=−13x−12\Rightarrow - 11y = - 13x - 12
Take -1 common on RHS side, then
⇒−11y=−1(13x+12)\Rightarrow - 11y = - 1\left( {13x + 12} \right)
Multiply both sides by -1
⇒11y=13x+12\Rightarrow11y = 13x + 12
To solve the equation for y by dividing 11 on both sides, then
⇒1111y=1311x+1211\Rightarrow\dfrac{{11}}{{11}}y = \dfrac{{13}}{{11}}x + \dfrac{{12}}{{11}}
∴ y=1311x+1211\therefore\,y = \dfrac{{13}}{{11}}x + \dfrac{{12}}{{11}}
Hence, the slope of intercept form of the line 13x−11y=−1213x - 11y = - 12 is  y=1311x+1211\,y = \dfrac{{13}}{{11}}x + \dfrac{{12}}{{11}} .
So, the correct answer is “  y=1311x+1211\,y = \dfrac{{13}}{{11}}x + \dfrac{{12}}{{11}} ”.

Note : The equation which is in the form of y=mx+by = mx + b , where m is slope and b is known as y-intercept. Slope means ratio of vertical change to the horizontal change i.e., ratio of change in y-axis or step size of y-axis to the change in x-axis or step size of x-axis. An intercept is a point where the straight line or a curve intersects the y-axis in a plane. If the point x is zero then the obtained point is a y -intercept.