Final answer:
An equation solver with slope and point is used to find the equation of a line by providing a method to plot the line with a given slope and a specific point through which the line passes. d) Find the equation of a line is correct answer.
Step-by-step explanation:
An equation solver with slope and point is used to find the equation of a line. This is because, given a slope and a specific point, one can determine the precise linear equation that represents the line passing through that point with the given slope. In the slope-intercept form of a linear equation, y = mx + b, m represents the slope and b represents the y-intercept.
In an alternative, but equivalent form, y = a + bx, a is the y-intercept and b is the slope. The concept of slope refers to the steepness of a line, calculated as the ratio of the vertical change ('rise') to the horizontal change ('run') between two points on the line. The y-intercept is a specific point where the line crosses the y-axis, expressed as (0, a).
To illustrate, in Figure A1 Slope and the Algebra of Straight Lines, the y-intercept is 9 and the slope is 3, indicating a rise of 3 in the y-value for every increase of 1 in the x-value. This demonstrates how the slope and y-intercept determine the shape and position of a line on a graph.