Final answer:
The correct equation that represents a line passing through the point (-4, -6) with a slope of 7/3 is y = 7/3x + 6 (Option C). This is determined by using the point-slope form and the given point to solve for the y-intercept.
Step-by-step explanation:
The question asks which equation represents a line passing through the point (-4, -6) and having a slope of 7/3. The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b are the y-intercept. To find the correct equation, we can use the slope and the given point to solve for b.
The slope is given as 7/3, so the equation will start with y = (7/3) x + b. Now we substitute x with -4 and y with -6:
-6 = (7/3) (-4) + b. Simplifying this, we have:
-6 = -28/3 + b.
To find b, we can add 28/3 to both sides of the equation: -18/3 + 28/3 = b, so 10/3 = b.
Now we have the value for b, which is 10/3. Thus, the equation of the line is y = (7/3) x + (10/3). We can find the correct equation by looking for the y-intercept in decimal form, which is approximately +3.33. The only equation that matches our slope of 7/3 and has a positive y-intercept is y = 7/3x + 6 (C).