Write an equation of a line that is parallel to the line y-3=2(x+5) and goes through the point (5,7)
5-3=2(7+5)
2=26
or
1=13
Using the same form of your given line, and since the slope is the same , m = 2
y-7 = 2(x-5)
or
y = 2x - 10 + 7
y = 2x- 3
To find the equation of a line that is parallel to a given line and passes through a given point, you need to follow these steps:
Step 1: Determine the slope of the given line.
The given line equation is in the form y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope of the line. In this case, the given line equation is y - 3 = 2(x + 5), which can be rewritten in slope-intercept form (y = mx + b) as y = 2x + 13, where the slope (m) is 2.
Step 2: Parallel lines have the same slope.
Since you want a line that is parallel to the given line, it must have the same slope as 2. Therefore, the equation of the line we are looking for will also have a slope of 2.
Step 3: Use the point-slope form to find the equation.
The point-slope form of a linear equation is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope. You have been given the point (5, 7). Using this, you can substitute the values into the point-slope form to find the equation:
y - 7 = 2(x - 5)
This is the equation of a line that is parallel to the given line y - 3 = 2(x + 5) and passes through the point (5, 7).