First, remember that if two lines are parallel, they have the same slope. The problem already gave us a point on the line and we now have the power to find the slope. Since we have the slope and a point on the line, we are going to find the equation of the line through the point-slope formula, which is:
[tex](y - y_1) = m(x - x_1)[/tex]
The equation given to us has a slope of 2, as we can see because the line is in slope-intercept form. Also, we are given the point (3, 11), which we are told is on the line. Since we are already given all of the information for the point-slope formula, we can simply substitute it in and solve for the equation.
[tex](y - 11) = 2(x - 3)[/tex]
[tex]y - 11 = 2x - 6[/tex]
[tex]y = 2x + 5[/tex]
The equation of our line is y = 2x + 5.
Slope-intercept form:
y = mx + b "m" is the slope, "b" is the y-intercept (the y value when x = 0)
For lines to be parallel, they have to have the SAME slope.
The given line's slope is 2, so the parallel line's slope is also 2.
y = 2x + b
To find "b", plug in the point (3,11) into the equation.
y = 2x + b
11 = 2(3) + b Multiply 2 and 3
11 = 6 + b Subtract 6 on both sides
5 = b
y = 2x + 5
