Question

find the equation of the line that is parallel to the line y=2x+9 and passes through the line (5,-10)

Answer 1

y = 2x - 20

Explanation:

General equation of a line is y = mx + b where m = slope and b = y-intercept

Parallel lines will have same slope but different intercepts

Given line: y = 2x + 9

Slope of this line is 2

Parallel line will have equation y = 2x + b

Since it passes through 5, 10 the value of y = - 10 must be the same as 2x+b for x = 5

Plugging in values:

- 10 = 2(5) + b

- 10 = 10 + b

-10-10 = b

b = - 20

So the equation of the line that is parallel to the line y=2x+9 and passes through the line (5,-10)

y = 2x - 20

Answer 2

Answer: the equation of the line that is parallel to y = 2x + 9 and passes through the point (5,-10) is y = 2x + 20

Explanation:

A line that is parallel to another line will have the same slope (m). The slope of the line y = 2x + 9 is m= 2.

To find the equation of the line that is parallel to y = 2x + 9 and passes through the point (5,-10), we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line, and m is the slope of the line.

So, the equation of the line that is parallel to y = 2x + 9 and passes through the point (5,-10) is:

y - (-10) = 2(x - 5)

Simplifying the equation:

y = 2x + 20

So, the equation of the line that is parallel to y = 2x + 9 and passes through the point (5,-10) is y = 2x + 20