The equation of a line in the slope-intercept form, parallel to the line y = 3, that passes through (0, 6) is y = 6.
What is the equation of a line?
The equation of a line is the representation of a line on a coordinate (x and y) plane, which shows the relation between x and y, for every point on the particular line.
The standard form of a line is ax + by = c, where x and y are variables and a, b, and c are constants.
The slope-intercept form of a line is y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept of the line.
How are slopes of parallel lines related?
If the slope of two parallel lines is m1 and m2, then m1 = m2.
How do we solve the given question?
We are informed that the equation of a line is y = 3. We are asked to write the equation of a line parallel to this line that passes through the point (0, 6).
Let the given line y = 3, be AB.
Let the required line be XY.
Comparing y = 3, with the slope-intercept form of a line y = mx + b, we can say that its slope, m1 = 0.
If we take the slope of the line XY as m2, then we know that m2 = m1, as XY is parallel to AB.
∴ m2 = 0.
Now, we can write the equation of the line XY as
y = m2*x + b.
or, y = 0(x) + b
or, y = b.
We put y = 6 in the above equation to get the value of b, as XY passes through the point (0, 6).
∴ 6 = b
or, b = 6.
Substituting the value of b = 6, in the equation above, we get the equation of the line XY as y = 6.
∴ The equation of a line in the slope-intercept form, parallel to the line y = 3, that passes through (0, 6) is y = 6.
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