Final answer:
The equation of the line that passes through the point (-3,0) with a slope of 4/3 is y = (4/3)x + 4.
Step-by-step explanation:
The question concerns finding the equation of a line that passes through a given point with a particular slope. This is a fundamental concept in algebra and coordinate geometry. The equation of a straight line in slope-intercept form is y = mx + b, where m represents the slope and b represents the y-intercept.
In this case, we are given a slope (m) of 4/3 and a point (-3,0) through which the line passes. To find the equation of the line, we use the point-slope form of the equation, which is (y - y1) = m(x - x1), where (x1, y1) is the given point. Substituting the given slope and point values, we get (y - 0) = (4/3)(x + 3). Simplifying the equation by distributing the slope on the right side, we get y = (4/3)x + 4. Thus, the equation of the line is y = (4/3)x + 4.