Question

The straight line L is parallel to the line with equation 2y+8x=5. L passes through the point (2,3) Find an equation for L.

Answer 1

To find the equation of the line parallel to the given line, we need to determine the slope of the given line first. The slope of the given line is -4. Using the point-slope form of a linear equation, we can write the equation of the line passing through (2, 3) as y = -4x + 11.

Step-by-step explanation:

To find the equation of the line parallel to the given line, we need to determine the slope of the given line first.

The equation of the given line is 2y + 8x = 5. To find the slope, we need to rearrange the equation to the form y = mx + b, where m is the slope.

Starting with 2y + 8x = 5:

1. Subtract 8x from both sides: 2y = -8x + 5
2. Divide all terms by 2: y = -4x + 5/2

Since the slope of parallel lines is equal, the slope of the line we are looking for is -4.

We also know that the line passes through the point (2,3). Therefore, we can use the point-slope form of a linear equation to write the equation of the line: y - y1 = m(x - x1).

Plugging in the values, we get y - 3 = -4(x - 2).

Simplifying the equation gives us the final equation: y = -4x + 11.

Answer 2

To find an equation for the line L that is parallel to the line with equation 2y + 8x = 5 and passes through the point (2, 3), we can use the point-slope form of a line. The equation for the line L is y - 3 = -4(x - 2).

Step-by-step explanation:

To find an equation for the line L that is parallel to the line with equation 2y + 8x = 5, we need to determine the slope of the given line. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. In order to find the slope, we need to rearrange the equation to isolate the y term:

2y + 8x = 5

2y = -8x + 5

y = -4x + 2.5

Now we can see that the slope of the given line is -4. Since the line L is parallel to this line, it must have the same slope. Using the point-slope form of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can substitute the given point (2, 3) and the slope -4 into the equation:

y - 3 = -4(x - 2)

This is the equation for the line L that is parallel to 2y + 8x = 5 and passes through the point (2, 3).