Question

find an equation of the line passing through the pair of points. write the equation in the form Ax+By=c

Answer 1

The points given:

`\begin{gathered} (x_1,y_1)=(0,0) \\ \text{and} \\ (x_2,y_2)=(-(1)/(7),(1)/(4)) \end{gathered}`

The slope, m, of the line can be found using the slope formula:

`m=(y_2-y_1)/(x_2-x_1)`

Substituting the points, we get:

`\begin{gathered} m=((1)/(4)-0)/(-(1)/(7)-0) \\ m=((1)/(4))/(-(1)/(7)) \\ m=(1)/(4)*-(7)/(1) \\ m=-(7)/(4) \end{gathered}`

The slope intercept form of a line is y = mx + b

We can now write:

`y=-(7)/(4)x+b`

We know, (0,0) is a point, so we substitute it and find b:

`\begin{gathered} y=-(7)/(4)x+b \\ 0=-(7)/(4)(0)+b \\ b=0 \end{gathered}`

The equation is:

`\begin{gathered} y=-(7)/(4)x \\ \text{Multiplying by 4, we get:} \\ 4y=-7x \\ In\text{ general form,} \\ 7x+4y=0 \end{gathered}`