Question

Look at the graph shown:
A coordinate plane is shown. A line passes through the y-axis at -1 and through the point 1 comma 2. Which equation best represents the line?
y = 1 over 3. x − 1
y = 3x − 1
y = −x + 1 over 3. y = 3x + 1

Answer 1

SOLUTION

A line passes through the y-axis at -1 and through the point (1, 2) . Which equation best represents the line

y = 1/3x − 1

y = 3x − 1

y = − x + 1/3

y = 3x + 1

EVALUATION

Here it is given that the line passes through the y-axis at -1

So the line passes through the point (0,-1)

Again the line passes through the point (1, 2)

So the required equation of the line is

$\displaystyle \sf{ \frac{y + 1}{x - 0} = \frac{2 + 1}{1 - 0} }$

$\implies \: \displaystyle \sf{ \frac{y + 1}{x } =3 }$

$\implies \: \displaystyle \sf{ y + 1 = 3x }$

$\implies \: \displaystyle \sf{ y = 3x - 1 }$

Hence the equation which best represents the line is

$\sf{y = 3x - 1}$

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Answer 2

$\huge \rm{ \underline{ \underline{ \color{navy}{Solution : - }}}}$

GIVEN THAT ➠

• The line passes through the y-axis at -1.

• The line passes through the point (0,-1).

• And again the line passes through the point (1, 2).

REQUIRED EQUATION OF THE LINE ➠

$\displaystyle \sf \boxed{ \color{royalblue}{ \frac{y + 1}{x - 0} = \frac{2 + 1}{1 - 0} }} \\ </p><p>{ \purple{\implies \: \displaystyle \sf{ \frac{y + 1}{x } =3 }}} \\ </p><p>{\pink{\implies \: \displaystyle \sf{ y + 1 = 3x }}}\\ </p><p>{\color{magenta}{\implies \: \displaystyle \sf{ y = 3x - 1 }}}$

HENCE THE EQUATION WHICH BEST REPRESENTS THE LINE IS ➠

$\sf \underline{\red{y = 3x - 1}}$