Question

each of the following lines has a slope and y-intercept that can be determined by examining the graph. for each state the slope, the y-intercept,and then write the equation in y=mx + b form

Answer 1

The straight line graphed has a y-intercept of 9 and a slope of 3, resulting in the equation
`y = 3x + 9`, which reflects the shape and position of the line on the graph.

According to FIGURE A1 on Slope and the Algebra of Straight Lines, the line that is graphed has a y-intercept of 9 and a slope of 3. This means that for every one unit of increase on the x-axis (horizontal axis), there is a rise of 3 units on the y-axis (vertical axis). The slope of a line is constant throughout; hence this line would increase by 3 units vertically for each single unit moved horizontally, no matter where you start on the line.

The equation of a straight line in
`y = mx+b` form is determined by its slope (m) and its y-intercept (b). In this case, since the slope (m) is 3 and the y-intercept (b) is 9, the equation of the line can be written as:

`y = 3x + 9`

This equation represents a straight line that crosses the y-axis at 9 and has a slope of 3, indicating its steepness and direction.