Final answer:
To find the equation of a line parallel to the given line that passes through the points (3, 0) and (0, 2), we can use the slope-intercept form.
Step-by-step explanation:
The given line is parallel to the line 4x+y-17=0. To find the equation of the line, we can use the slope-intercept form, which is y = mx + b. We are given that the line has an x-intercept of 3, meaning it passes through the point (3, 0). We are also given that the line has a y-intercept of 2, meaning it passes through the point (0, 2). Using these two points, we can find the slope of the line and substitute it into the slope-intercept form to determine the equation.
The slope of the line can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, (x1, y1) = (3, 0) and (x2, y2) = (0, 2). Plugging these values into the formula, we get m = (2 - 0) / (0 - 3) = 2 / -3 = -2/3. Therefore, the slope of the line is -2/3.
Now that we have the slope, we can substitute it into the slope-intercept form, along with the known y-intercept of 2, to find the equation of the line. The equation will be y = (-2/3)x + 2.