Question

What is the equation of the line that goes through the point (6,-1) and is parallel to the line represented by the equation below?

y=-5/6 x+3

A. y= -5/6x + 4
B. y= -5/6x - 6
C. y= -5/6x -4
D. y= -5/6x + 6

Answer 1

y = -5/6x + 4 (slope - intercept form)

OR

5x + 6y -24 = 0 (standard form)

Explanation:

What is the equation of the line that goes through the point (6,-1) and is parallel to the line represented by the equation below?

y=-5/6 x+3

To solve this;

We need to first find the slope of the the equation given

Comparing the equation given with y=mx + c, the slope (m) = -5/6, any equation parallel to this equation will have the same slope as this equation.

Since our new equation is said to be parallel to this equation the slope(m) of our new equation is also -5/6.

Now we will proceed to find the intercept of our new equation, to find the intercept, we will simply plug in the value of the points given and the slope into the formula y=mx + c and then simplify

The value of the points given are; (6, -1) which implies x=6 and y=-1 slope(m)= -5/6

y = mx + c

-1 = -5/6 (6) + c

-1 = -5 + c

Add 5 to both-side of the equation to get the value of c

-1+5 = -5+5 + c

4 = c

c=4

Therefore the intercept(c) of our new equation is 4

We can now proceed to form our new equation. To form the equation, all we need to do is to simply insert the value of our slope (m) and intercept (c) into y = mx + c

y = -5/6x + 4

This above equation is in slope-intercept form, we can further simplify it to be in the standard form.

6y = -5x + 24

5x + 6y -24 = 0

Answer 2

`\huge{\boxed{y=-(5)/(6) x+4}}`

Parallel lines share the same slope, so the slope of the parallel line in this case must be
`-(5)/(6)`.

Point-slope form is
`y-y_1=m(x-x_1)`, where
`m` is the slope and
`(x_1, y_1)` is any known point on the line.

Plug in the values.
`y-(-1)=-(5)/(6) (x-6)`

Simplify and distribute.
`y+1=-(5)/(6) x+5`

Subtract 1 from both sides.
`\boxed{y=-(5)/(6) x+4}`