The equation of line AB is y = 2x + 4. Write an equation of a line parallel to line AB in slope-intercept form that contains point (3, -2).
m = 2
-2 = 2 (3) + b
-2 = 6 + b
b = -8
so
y = 2 x - 8
To write an equation of a line parallel to line AB, we need to use the same slope as line AB. In this case, the slope of line AB is 2.
Using the point-slope form of a linear equation, we can write the equation of the line as:
y - y1 = m(x - x1),
where (x1, y1) represents the coordinates of the given point (3, -2), and m represents the slope.
Plugging in the values, we have:
y - (-2) = 2(x - 3).
Simplifying the equation further:
y + 2 = 2x - 6.
Now, we can rearrange the equation to slope-intercept form (y = mx + b), where b represents the y-intercept:
y = 2x - 6 - 2.
Combining like terms, we get:
y = 2x - 8.
Therefore, the equation of the line parallel to line AB in slope-intercept form that contains the point (3, -2) is y = 2x - 8.
To find the equation of a line parallel to line AB in slope-intercept form that contains point (3, -2), you first need to determine the slope of line AB.
The equation of line AB is given as y = 2x + 4, which is in the slope-intercept form y = mx + b. From this equation, you can determine that the slope of line AB is 2.
Since the line you want to find is parallel to line AB, it will have the same slope of 2. Therefore, the equation of the line you are looking for can be written in the form y = 2x + b, where b is the y-intercept of the line.
To find the value of b, you can substitute the coordinates of the given point (3, -2) into the equation y = 2x + b and solve for b.
-2 = 2(3) + b
-2 = 6 + b
b = -8
Therefore, the equation of the line parallel to line AB in slope-intercept form that contains the point (3, -2) is y = 2x - 8.