Question

Reduce the equation $y + 5 = 0$ to slope-intercept form, and hence find the slope and the y-intercept of the line.

Answer 1

Hint : To find slope and y intercept of given equation we first write given equation in standard form by adding ‘ $0x$ ’ to given equation and then on comparing given equation with standard form to find respective value of ‘m’ and ‘c’.

Complete step-by-step answer :
Slope intercept form of line is given as $y = mx + c$ , where ‘m’ is the slope of the line and ‘c’ is the intercept that a line makes with the y-axis.
Equation of the line is obtained with the help of slope of line that is why it is called as slope intercept form.
In this form ‘m’ stands for slope of the line and ‘c’ stands for the intercept that a line makes with the y-axis.
The equation of the line in the statement is $y + 5 = 0$ .
It is required to reduce a given line in slope intercept form.
For this we see that there is no ‘x’ term in a given equation of line but there is ‘x’ term in standard slope intercept form of a line.
Hence, to introduce ‘x’ term we add ‘ $0x$ ’ in the given equation of line as on adding it to the line it won’t disturb the equation.
Therefore, given equation becomes $y + 5 + 0x = 0$ or we can write it as
$y + 0x + 5 = 0 \\\ or \\\ \,y + 0x = - 5 \\\$
From above we see that $y + 0x = - 5$ is the required slope intercept form of the given equation.
Now, for finding value of slope and intercept of given equation we equate above form a given line with standard slope form.
On equating both lines we have m = $0$ which implies that the slope of the given line is zero. Hence, a given line is parallel to the x-axis as its slope is zero and it implies that the given line doesn't meet the x-axis.
Also, the value of ‘c’ of a given line is $- 5$ .
Which implies that y -intercept of the given line is $- 5$ .
Hence, from above we see that slope and y – intercept of given line are $0$ and $- 5$ respectively.

Note : As, we know that there are different form of line 1st is one point and slope form\left\\{ {y - {y_1} = m\left( {x - {x_1}} \right)} \right\\}, 2nd is two point form \left\\{ {y - {y_1} = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\left( {x - {x_1}} \right)} \right\\} and 3rd is slope intercept form \left\\{ {y = mx + c} \right\\} . So, one should be very careful regarding choosing the form of line which is required in the given question to get slope and y intercept.