Final answer:
The equation of a line with a slope of 2 that crosses the y-axis at -3 is y = 2x - 3, making the correct answer a. y = 2x - 3.
Step-by-step explanation:
To find the equation of a line that goes up two spaces for every space it goes over and crosses the y-axis at -3, we need to identify two key components of the equation of a straight line: its slope (m) and y-intercept (b). The slope represents the rate at which the line rises or falls as it moves along the x-axis, and the y-intercept is the value of y where the line crosses the y-axis.
In this case, the line goes up two spaces for each space it goes over, which means that the slope (m) is 2, since the rise/run ratio is 2/1. The line crosses the y-axis at -3, which indicates that the y-intercept (b) is -3. Using the slope-intercept form of a line, which is y = mx + b, we can plug in our values to get the correct equation for the line: y = 2x - 3.Therefore, the correct answer is a. y = 2x - 3.