# 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

Verified

385.2k+ views

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.

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.

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