Question

Question #ecc2a

Answer 1

`y=5x+6`

Explanation:

`• " parallel lines have equal slopes"`

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`y=5x-3" is in this form"`

`"with "m=5`

`rArry=5x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute "(-2,-4)`
`"into the partial equation"`

`-4=-10+brArrb=-4+10=6`

`rArry=5x+6" is equation of parallel line"`

Answer 2

The equation of the given line
`y=5x-3`

Since the line we are asked to find is parallel to the given line, their slope must be equal.

The slope of the given line`=`The slope of the unknown line`=5`

( I hope you know how to find the slope using the equation of the line)

Now,
The unknown line also passes through `(-2,-4)`

Applying the Point-Slope Form,
`y-y_1 = m(x-x_1)`

where,
`(x_1,y_1)` are the coordinates of the point that lies on the line.

`(y+4) = 5(x+2)`

`5x -y +6=0`

Answer 3

`y=5x+6`

Explanation:

If two line are parallel, then they have he same gradient:

Gradient of `y=5x-3` is 5.

Equation of a line:

`y_2-y_1=m(x_2-x_1)`

Equation of line passing through point `( -2 , -4 )`

`y-(-4)=5(x-(-2)`

`y+4=5(x+2)`

`y+4=5x+10`

`y=5x+6`

Graph: