The points given:
[tex]\begin{gathered} (x_1,y_1)=(0,0) \\ \text{and} \\ (x_2,y_2)=(-\frac{1}{7},\frac{1}{4}) \end{gathered}[/tex]
The slope, m, of the line can be found using the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting the points, we get:
[tex]\begin{gathered} m=\frac{\frac{1}{4}-0}{-\frac{1}{7}-0} \\ m=\frac{\frac{1}{4}}{-\frac{1}{7}} \\ m=\frac{1}{4}\times-\frac{7}{1} \\ m=-\frac{7}{4} \end{gathered}[/tex]
The slope intercept form of a line is y = mx + b
We can now write:
[tex]y=-\frac{7}{4}x+b[/tex]
We know, (0,0) is a point, so we substitute it and find b:
[tex]\begin{gathered} y=-\frac{7}{4}x+b \\ 0=-\frac{7}{4}(0)+b \\ b=0 \end{gathered}[/tex]
The equation is:
[tex]\begin{gathered} y=-\frac{7}{4}x \\ \text{Multiplying by 4, we get:} \\ 4y=-7x \\ In\text{ general form,} \\ 7x+4y=0 \end{gathered}[/tex]
