write an equation in slope intercept form for a line containing (5,3) that is parallel to the line y+11= 1/2 (4x+6)
parallel lines have similar equations, but different x/y intercepts
y = 2x + b
plug in the given point to find b
Why did the line stay home? Because it was parallel to all the other lines!
To find the equation of a line parallel to another line, we need to know that parallel lines have the same slope (the number multiplying the x term).
First, let's rewrite the given line, y + 11 = (1/2)(4x + 6), in slope-intercept form (y = mx + b):
y + 11 = 2x + 3
y = 2x + 3 - 11
y = 2x - 8
Since our parallel line has the same slope as the given line, the slope of the line we're looking for is also 2. Thus, our equation will be in the form y = 2x + b, where b is the y-intercept.
We're given that the parallel line contains the point (5,3). Plugging these coordinates into the equation, we can solve for b:
3 = 2(5) + b
3 = 10 + b
b = 3 - 10
b = -7
So, the equation of the line parallel to y + 11 = (1/2)(4x + 6) and containing the point (5,3) is:
y = 2x - 7
To find an equation in slope-intercept form for a line parallel to y + 11 = 1/2 (4x + 6) and passing through the point (5, 3), we need to determine the slope of the given line.
The equation y + 11 = 1/2 (4x + 6) is already in slope-intercept form (y = mx + b), where m represents the slope. By rearranging the equation, we can find the value of m:
y + 11 = 1/2 (4x + 6)
y = 1/2 (4x + 6) - 11
y = 1/2 * 4x + 1/2 * 6 - 11
y = 2x + 3 - 11
y = 2x - 8
The slope (m) of this line is 2.
Since lines that are parallel have the same slope, the equation we are looking for will also have a slope of 2. Using the point-slope form of a linear equation (y - y1 = m(x - x1)), we can substitute the given values to find the equation:
y - y1 = m(x - x1)
y - 3 = 2(x - 5)
Expanding the equation further:
y - 3 = 2x - 10
y = 2x - 10 + 3
y = 2x - 7
Therefore, the equation in slope-intercept form for the line containing (5, 3) and parallel to y + 11 = 1/2 (4x + 6) is y = 2x - 7.
To find the slope intercept form of a line, we need to determine the equation in the form of y = mx + b, where m represents the slope and b represents the y-intercept.
First, let's rewrite the given equation y + 11 = 1/2(4x + 6) in slope-intercept form:
Distribute 1/2 to (4x + 6)
y + 11 = 2x + 3
Subtract 11 from both sides
y = 2x + 3 - 11
y = 2x - 8
Now, we know that the line we are looking for is parallel to this line and contains the point (5, 3). Since parallel lines have the same slope, the slope of this line is 2. So we can use the slope-intercept form y = mx + b and substitute the values of the slope and the given point to find the equation.
y = mx + b
3 = 2(5) + b
Now solve for b by simplifying the expression:
3 = 10 + b
b = 3 - 10
b = -7
Therefore, the equation of the line that is parallel to y + 11 = 1/2(4x + 6) and contains the point (5, 3) is:
y = 2x - 7