find the equation of the line that contains the given point and is paralell to the given line

Question

1. (-3,5), y=-2x+1

 

 

2.(2,8), y=4x-1

Answer 1

Hi Mondrea;

1. (-3,5), y=-2x+1

The equation is parallel to this.  This means that the slope is identical.  This formula is in the format of...

y=mx+b

m is the slope, -2 in this equation, as well as the line parallel to it.

b is the y-intercept, the value of y when x=0.

We will use point-slope formula to establish the equation of the line parallel to this.

y-y₁=m(x-x₁)

y-5=-2(x--3)
Subtracting a negative number is the same as adding a positive number...

y-5=(-2)(x+3)

y-5=-2x-6

Let's add 5 to both sides...

5+y-5=-2x-6+5

y=-2x-1

2.(2,8), y=4x-1

Slope is 4.

(y-y₁)=m(x-x₁)

(y-8)=4(x-2)

y-8=4x-8

The -8 on both sides cancels...

y=4x

Answer 2

Mondrea, using cartesian (x-y) coordinates lines are parallel if their equations have the same slope. So the slope of the first line is -2, so the slope of a line parallel to it has to also be negative -2.  Using the point-slope [(y - y1) = m (x - x1)] equation for a line with a slope of -2 and the point (-3,5), the equation would be
y - 5 = -2 [x - (-3)] or y - 5 = -2 (x + 3) or in slope-intercept (y = mx +b) form y = -2x - 1

 

You can repeat this process for your second problem in the exact same way.  I hope this helps.  John