Question

Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the following equation.

Point: (3,1)
Equation: 2x+y=5

Answer 1

To find the equation of a line that is parallel to the given equation 2x + y = 5 and passes through the point (3,1), we need to use the same slope as the given equation. The equation of the line is y = -2x + 7.

Step-by-step explanation:

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

To find the equation of a line that is parallel to the given equation and passes through the point (3,1), we need to use the same slope as the given equation.

The given equation is 2x + y = 5. To write it in slope-intercept form, we need to solve for y.

1. Subtract 2x from both sides to get y = -2x + 5.
2. Since the line we want is parallel to this line, it will have the same slope, -2.
3. Now we can plug in the slope and the coordinates of the given point (3,1) into the slope-intercept form equation: y = -2x + b.
4. Substituting the point (3,1), we get 1 = -2(3) + b.
5. Simplify the equation: 1 = -6 + b
6. Add 6 to both sides: 7 = b.

Therefore, the equation of the line that is parallel to 2x + y = 5 and passes through the point (3,1) is y = -2x + 7.