find the equation of a line parallel to y - 5x = 10 that passes through the point (3, 10). (answer in slope-intercept form)

y = 5x - 5 is the equation of a line parallel to y - 5x = 10 that passes through the point (3, 10) in slope intercept form

Solution:

Given that line parallel to y - 5x = 10 that passes through the point (3, 10)

To find: equation of line in slope intercept form

The slope intercept form is given as:

y = mx + c

Where "m" is the slope of line and "c" is the y - intercept

Let us first find slope of line

y - 5x = 10

y = 5x + 10

On comparing y = 5x + 10 with slope intercept form, we get m = 5

Thus slope of given line is 5

We know that slopes of parallel lines are equal

So the slope of line parallel to given line is also 5

Now we have to find the equation of line with slope m = 5 and passes through point (3, 10)

Substitute m = 5 and (x, y) = (3, 10) in slope intercept form,

10 = 5(3) + c

10 = 15 + c

c = - 5

Thus the required equation is:

Substitute c = -5 and m = 5 in eqn 1

y = 5x - 5

Thus the required equation of line is found