Question

Reduce the following equations into slope intercept form and find their slopes and the $y$ -intercept.

$$(i).{\text{ x + 7y = 0}} \\\ (ii).{\text{ 6x + 3y - 5 = 0}} \\\ (iii).{\text{ y = 0}} \\\$$

Answer 1

Hint- Convert the given equation into general form and compare with the general formula.

We know that
General slope intercept form of a line is given by the equation:
$y = mx + c$
Where
$m =$ Slope of the line
$c =$ Y-intercept of the line
Now converting the given equation in the general form and then comparing
$(i){\text{ x + 7y = 0}} \\\ \Rightarrow {\text{7y = - x}} \\\ \Rightarrow {\text{y = }}\dfrac{{ - 1}}{7}{\text{x}} \\\ \Rightarrow {\text{y = }}\dfrac{{ - 1}}{7}{\text{x + 0}} \\\$
So after comparing with the general equation.
Hence, Slope$= \dfrac{{ - 1}}{7}$ and Y-intercept$= 0$
${\text{(}}ii{\text{) 6x + 3y - 5 = 0}} \\\ \Rightarrow {\text{3y = - 6x + 5}} \\\ \Rightarrow {\text{y = }}\dfrac{{ - 6}}{3}{\text{x + }}\dfrac{5}{3} \\\ \Rightarrow {\text{y = - 2x + }}\dfrac{5}{3} \\\$
So after comparing with the general equation.
Hence, Slope$= - 2$ and Y-intercept$= \dfrac{5}{3}$
$(iii){\text{y = 0}} \\\ \Rightarrow {\text{y = 0x + 0}} \\\$
So after comparing with the general equation.
Hence, Slope$= 0$ and Y-intercept$= 0$

Note- Conversion of equation of the line to slope intercept form is done by simple manipulation of equation. Y-intercept of the line is the point where the line cuts the y-axis and slope is the tan of angle made by the line on the x-axis.