Question

Find an equation of the line passing through the point (5,4) and parallel to the line whose equation is 2x+y=3

Answer 1

The equation of the line parallel to 2x + y = 3 and passing through the point (5, 4) is y = -2x + 14.

Step-by-step explanation:

To find the equation of a line that is parallel to the given line 2x + y = 3 and passes through the point (5, 4), we first need to put the given line into slope-intercept form (y = mx + b), where m represents the slope and b the y-intercept. For the equation 2x + y = 3, we solve for y to get y = -2x + 3, which shows that the slope (m) is -2. Since parallel lines have the same slope, our new line will also have a slope of -2.

Using the point-slope form (y - y1 = m(x - x1)), where (x1, y1) is the point (5, 4) and m is -2, we get y - 4 = -2(x - 5). Simplifying this, y - 4 = -2x + 10, which leads to y = -2x + 14 as the equation of the line passing through (5, 4) and parallel to 2x + y = 3.

Answer 2

Step-by-step explanation:

Use the point-slope formula.

y - y_1 = m(x - x_1) you have : x_1 =5 and y_1 =4

m the slope m= -2 (same slope for the line : 2x+y=3 because this lines are parallel and you can write y=-2x+3

an equation for this line is : y-4 = -2(x-5)