Final answer:
To find the equation of a line parallel to the line 3x + 5y = 35 and passing through the point (-5,4), use the point-slope form of a linear equation.
Step-by-step explanation:
To find the equation of a line parallel to the line 3x + 5y = 35, we need to determine the slope of the given line. We can rewrite the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Rearranging the equation, we have 5y = -3x + 35, and dividing by 5, we get y = -3/5x + 7.
The slope of this line is -3/5, so any line parallel to it will also have a slope of -3/5.
Since the line we want passes through the point (-5,4), we can use the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Plugging in the values, we have y - 4 = -3/5(x - (-5)), simplifying further gives y - 4 = -3/5(x + 5).
Expanding, we get y - 4 = -3/5x - 3, and rearranging the equation, we obtain y = -3/5x + 1.