Question

Line equations from point/slope calculator

A) Slope-Intercept Form
B) Point-Slope Form
C) Standard Form
D) Intercept Form

Answer 1

The line equations from the point/slope calculator include Slope-Intercept Form, Point-Slope Form, Standard Form, and Intercept Form.

Step-by-step explanation:

The line equations from the point/slope calculator are:

1. A) Slope-Intercept Form: The equation is in the form y = mx + b, where m represents the slope and b represents the y-intercept.
2. B) Point-Slope Form: The equation is in the form y - y1 = m(x - x1), where m represents the slope and (x1, y1) represents a point on the line.
3. C) Standard Form: The equation is in the form Ax + By = C, where A and B are coefficients and C is a constant.
4. D) Intercept Form: The equation is in the form x/a + y/b = 1, where a and b are the x-intercept and y-intercept respectively.

The question focuses on understanding the different forms of linear equations and the components that determine their graphs, such as slope and y-intercept. In the slope-intercept form (y = mx + b or y = a + bx), 'm' or 'b' represents the slope, indicating the steepness of the line, while 'b' or 'a' signifies the y-intercept, which is where the line crosses the y-axis.

From the information given, if we have a line that intersects the y-axis at 9 (y-intercept = 9) and has a slope of 3, it means for every unit increase in x, y increases by 3 units. The slope-intercept equation of this line would be y = 3x + 9. In the context of the practice test question provided, options A (y = -3x), B (y = 0.2 +0.74x), and C (y = -9.4 - 2x) are all linear, but it mentions to choose from A and B.