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

The equation of the required line is .

Given:

The eqation of paralle line is . The required line passes through the point .

To find:

The equation of the required line in slope-intercept form.

Explanation:

The given equation can be rewritten as:

On comparing this equation with , we get

Slopes of parallel lines are always equal.

The slope of reqired line is and it passing through the point . Using the point slope form, the equation of the line is:

Therefore, the equation of the required line is .

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Y - 5x = 10 can be written in the slope-intercept form as
y = 5x + 10

The slope-intercept form is y = mx + b, where m = slope, and b = y-intercept.

In this case, the 5 is the slope.

Parallel lines have equal slopes, so the line we need to find also has a slope of 5. Its equation is

y = 5x + b

We need to find what b is.

We can use the given point, (3, 10), in for x and y and solve for b.

10 = 5 * 3 + b

10 = 15 + b

-5 = b

Now that we know that b = -5, we replace b with -5 to get our equation

y = 5x - 5

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