Hello!
Because we have been asked to write the equation of a line, we will need to give the answer in slope-intercept form. Slope-intercept form uses the following formula:
y = mx + b
In the above formula, M represents the slope while B represents the y-intercept. We are asked to write the equation of a horizontal line that passes through the given point. Horizontal lines have a slope of zero (0), so we’ll begin by inserting this value into the slope-intercept formula:
y = (0)x + b
Now simplify the right side of the equation:
y = b
Now we must find the y-intercept of the line in question. We are given that it passes through point (0,3). We know that any point taking the form (0,y) lies on the y-axis and, consequently, can be classified as a y-intercept. Therefore, the y-intercept of the given line must be 3. Insert this value into the simplified equation above:
y = b
y = (3)
We have now proven that the equation of the given line is (y = 3).
I hope this helps!
