Final answer:
The point-slope form of the equation y=1/2x-3, using the y-intercept (0, -3) and the slope of 1/2, is y + 3 = 1/2x. In geometry, a line is a one-dimensional figure since it has length but no width. A line is made of a set of points that is extended infinitely in opposing directions.
Step-by-step explanation:
The equation y=1/2x-3 is already in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. To convert it to point-slope form, we need a point on the line and the slope. We can use the y-intercept as our point, which is (0, -3), and the slope is 1/2 as given in the equation. The point-slope form of the equation is y - y1 = m(x - x1), where (x1, y1) is the point on the line. Plugging in our values, the point-slope form is y - (-3) = 1/2(x - 0), which simplifies to y + 3 = 1/2x.
In geometry, a line is a one-dimensional figure since it has length but no width. A line is made of a set of points that is extended infinitely in opposing directions. Two points in a two-dimensional plane determine it. However, there are different forms of equations of a line in a two-dimensional coordinate plane. The three mainly used methods are point-slope form, slope-intercept form, and general or standard form of the equation of a line.
As the name suggests, the point-slope form involves the straight-line slope and a point on the line. It is possible to write the equations of infinite lines with a given slope, but we get a unique straight line when we specify that the line passes through a given point. Thus, only a point on the line and its slope is required to determine the equation of a straight line in the point-slope form.