find the slope of a line parallel to the graph of each equation : y = 2/7x + 1

Question

 

Write an equation for the line that is parallel to the given line and that passes through the given point.
(3,4) y = 2x - 7

Answer 1

The graph of each equation : y = 2/7x + 1

The slope is m =  x-coeficient :2/7

Two lines are parallel then the slopes are equal.

The slope of a line parallel to the graph of each equation : y = 2/7x + 1 is m = 2/7

The equation of a line : y = 2x - 7

The slope of a line : m = x-coeficient =2

Two lines are parallel then the slopes are equal.

There fore parallel line slope : m = 2

Passes through the point (3, 4)

The point (x1,y1) and slope m then the equation of a line : y  - y1 = m(x  - x1)

Substitute values  x1 = 3 , y1= 4 and m = 2

There fore equation of a parallel line : y - 4 = 2(x - 3)

Distributive property a(b - c) = ab - ac a,b and c are any numbers

y - 4 = 2x - 6

Add 4 to each side

y - 4 + 4 = 2x - 6 +4

y = 2x - 2.

Answer 2

the slope intercept form line equation is y = mx + b. m is slope and b is y intercept.

y = 2/7x + 1 

slope = 2/7.

2.

the line is parallel to the line y = 2x - 7, so slope is same and slope = 2

the line equation is y = 2x + b

find b value by replacing the (x, y) with (3, 4)

4 = 2 * 3 + b

b = -2

the line equation is y = 2x - 2