Final answer:
The equation of the line that passes through (-2, 0) and is parallel to the given line 5x - 3y = -17 is y = 5/3x + 10/3.
Step-by-step explanation:
To find the equation of the line that is parallel to the line represented by 5x - 3y = -17 and passes through (-2, 0), we need to determine the slope of the given line. We can rearrange the equation 5x - 3y = -17 to slope-intercept form by isolating y. Subtracting 5x from both sides gives us -3y = -5x - 17. Dividing by -3, we get y = 5/3x + 17/3. The slope of this line is 5/3.
Since the slope of a line parallel to another line is the same, the slope of the line we are looking for is also 5/3. Now, we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point through which the line passes. Plugging in the values (-2, 0) for (x1, y1) and 5/3 for m, we get y - 0 = 5/3(x - (-2)). Simplifying, we have y = 5/3x + 10/3. This equation is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Therefore, the equation of the line that passes through (-2, 0) and is parallel to the line represented by 5x - 3y = -17 is y = 5/3x + 10/3.