Final answer:
False, point-slope form does not automatically provide the y-intercept. It provides the slope and requires rearrangement into slope-intercept form to determine the y-intercept.
Step-by-step explanation:
The student inquired whether it's true that equations in point-slope form always provide the slope and y-intercept. Point-slope form is typically written as y - y1 = m(x - x1), where (x1, y1) represents a specific point on the line and m represents the slope.
This form immediately gives the slope, but not directly the y-intercept. To find the y-intercept from a point-slope equation, one must rearrange it into the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
As an example, consider the slope-intercept form y = a + bx, where b represents the slope and a represents the y-intercept.
When we look at a graph of a line, the point where the line crosses the y-axis is the y-intercept and is symbolized by a, while the steepness or incline of the line, referred to as the slope, is symbolized by b.
The slope is constant along a straight line, indicating a fixed increase in y for each incremental increase in x.
The correct answer is Option 2: False.