Mathematics: What is an equation in slope-intercept form of the line that passes through (6, 10) and is parallel to the graph of y=1/3x−1?

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What is an equation in slope-intercept form of

vontie

08.02.2022

Given:

The equation of line is

$y=\dfrac{1}{3}x-1$

To find:

The equation of line in slope-intercept form parallel to given line and passes through (6,10).

Solution:

The slope intercept form of a line is

y=mx+b ...(i)

where, m is slope and b is y-intercept.

The equation of given line is

$y=\dfrac{1}{3}x-1$ ...(ii)

On comparing (i) and (ii), we get

$m=\dfrac{1}{3}$

Slope of given line is $\dfrac{1}{3}$ .

We know that slope of parallel lines are same. So, the slope of required line is $\dfrac{1}{3}$ .

Since slope of required line is $\dfrac{1}{3}$ and it passes through (6,10), therefore the equation of line is

y-y_1=m(x-x_1)

$y-10=\dfrac{1}{3}(x-6)$

$y-10=\dfrac{1}{3}(x)-\dfrac{1}{3}(6)$

$y-10=\dfrac{1}{3}(x)-2$

Add 10 on both sides.

$y-10+10=\dfrac{1}{3}(x)-2+10$

$y=\dfrac{1}{3}(x)+8$

Therefore, the required equation of line is $y=\dfrac{1}{3}(x)+8$ .

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