Question

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

Answer 1

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

Answer 2

The equation of the required line is $y=5x-5$.

Given:

• The eqation of paralle line is $y-5x=10$.

• The required line passes through the point $(3,10)$.

To find:

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

Explanation:

The given equation can be rewritten as:

$y=5x+10$

On comparing this equation with $y=mx+b$, we get

$m=5$

Slopes of parallel lines are always equal.

The slope of reqired line is $m=5$ and it passing through the point $(3,10)$. Using the point slope form, the equation of the line is:

$y-y_1=m(x-x_1)$

$y-10=5(x-3)$

$y=5x-15+10$

$y=5x-5$

Therefore, the equation of the required line is $y=5x-5$.

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