Answer:
[tex]y -7 = -\frac{7}{5}(x-5)[/tex]
or
[tex]y = -\frac{7}{5}x +14[/tex]
Step-by-step explanation:
Parallel lines are lines which have the same slope. To write the equation of the line parallel, find the slope of the equation 7x + 5y = 12 through conversion into slope intercept form.
7x + 5y = 12 becomes y = -7/5x + 12/5. The slope is -7/5.
Substitute\ m =-7/5 and the point (5,7) into the slope intercept form.
[tex]y-y_1=m(x-x_1)\\y -7= -\frac{7}{5}(x - 5)[/tex]
Convert the equation to slope intercept form by applying the distributive property.
[tex]y -7 = -\frac{7}{5}(x-5)\\y -7 = -\frac{7}{5}x +7\\y = -\frac{7}{5}x +7+7\\y = -\frac{7}{5}x +14[/tex]
