Final answer:
To write an equation of a line with a given slope and x-intercept, we use the general form of a linear equation and find the y-intercept using a point on the line that lies on the x-axis. Thus, the equation of the line with a slope of 2/3 and x-intercept of -6 is y = 2/3x + 4.
Step-by-step explanation:
To write an equation of a line with a given slope and x-intercept, we first need to understand the general form of a linear equation, which is y = mx + b. In this form, m represents the slope and b represents the y-intercept.
Given that the slope is 2/3 and the x-intercept is -6, we know that the point (-6, 0) lies on the line. We can use this point to find the y-intercept. Using the formula y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we can substitute the values into the equation to find the y-intercept. Thus, the equation of the line is y = 2/3x + 4.