Write an equation of the line with a y-intercept of 24 that is
parallel to 6x-2y=13.
NOPE, the robot tutor screws up again.
the y-intercept of 6x - 2y = -11 would be 11/2
correct way:
the old line is 6x - 2y = 13
So the new line must have the form 6x - 2y = c , only the constant would
change since the two lines are to be parallel.
but the point (0,24) must lie on it, so
6(0) - 2(24) = c
c = -48
new line : 6x - 2y = -48 , or in a better form:
3x - y = -24
To find the equation of a line that is parallel to a given line, we need to know that parallel lines have the same slope.
Step 1: Convert the given equation to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Let's now simplify the given equation, 6x - 2y = 13:
-2y = -6x + 13 (subtract 6x from both sides)
y = 3x - 6.5 (divide every term by -2)
So, the slope of the given line is 3.
Step 2: Use the slope-intercept form equation (y = mx + b) and the given y-intercept (b=24) to create the new equation.
We know that the new line will have a y-intercept of 24, so we can plug this value into the equation.
y = 3x + 24
Therefore, the equation of the line with a y-intercept of 24 that is parallel to 6x-2y=13 is y = 3x + 24.
To find the equation of a line that is parallel to the given line, we need to determine the slope of the given line first. The given equation is in the form of Ax + By = C, where the slope can be determined by rearranging the equation in slope-intercept form.
Let's rearrange the given equation 6x - 2y = 13 to slope-intercept form:
-2y = -6x + 13
y = 3x - 13/2
The slope of the given line is 3, as it is the coefficient of x.
Since the line we want to find is parallel to this line, it will also have a slope of 3.
The equation now takes the form of y = mx + b, where m is the slope and b is the y-intercept. We are given that the y-intercept is 24.
Substituting the given values into the equation, we get:
y = 3x + 24
Therefore, the equation of the line with a y-intercept of 24 that is parallel to 6x - 2y = 13 is y = 3x + 24.