Question

A) The equation of a line parallel to 6x – 2y + 10 = 0 and passes through the point
(-2, 7).

Answer 1

Answer: y = 3x + 13

Step-by-step explanation:

Rearrange the equation to slope-intercept form:

`6x - 2y + 10 = 0\\\\-2y=-6x-10\\\\y=(-(1)/(2) )(-6x-10)\\\\y=3x+5 \left \{ {{slope=3} \atop {y-intercept=5}} \right.`

A parallel line shares the same slope:

`y=3x+b`

Substitute in the given point to find the y-intercept(b):

`y=3x+b\\\\7=3(-2)+b\\\\7=-6+b\\\\b=7+6=13`

Therefore, the equation of the parallel line is:

`y=3x+13\\`