Question

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

Answer 1

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
  \[ \Rightarrow 13x - 11y = - 12\]
As we know the equation of a line in slope-intercept form is y=mx+b.
Rearrange the given equation of line \[13x - 11y = - 12\] in to the slope intercept form.
Subtract 13x from both sides, then
 \[ \Rightarrow13x - 13x - 11y = - 13x - 12\]
 \[ \Rightarrow - 11y = - 13x - 12\]
Take -1 common on RHS side, then
 \[ \Rightarrow - 11y = - 1\left( {13x + 12} \right)\]
Multiply both sides by -1
 \[ \Rightarrow11y = 13x + 12\]
To solve the equation for y by dividing 11 on both sides, then
 \[ \Rightarrow\dfrac{{11}}{{11}}y = \dfrac{{13}}{{11}}x + \dfrac{{12}}{{11}}\]
 \[\therefore\,y = \dfrac{{13}}{{11}}x + \dfrac{{12}}{{11}}\]
Hence, the slope of intercept form of the line \[13x - 11y = - 12\] is \[\,y = \dfrac{{13}}{{11}}x + \dfrac{{12}}{{11}}\] .
So, the correct answer is “ \[\,y = \dfrac{{13}}{{11}}x + \dfrac{{12}}{{11}}\] ”.

Note: The equation which is in the form of \[y = mx + b\] , 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.