Final answer:
The equation for the line passing through (-4,7) and parallel to the line 8x−3y−4=0 is 8x−3y+53=0.
Step-by-step explanation:
To find the equation of a line parallel to another line, we need to determine the slope of the given line.
The equation of the given line is 8x - 3y - 4 = 0.
To find the slope, we can rearrange the equation in slope-intercept form, which is in the form y = mx + b, where m is the slope. So, rearranging the equation, we get:
8x - 3y = 4
-3y = -8x + 4
y = (8/3)x - (4/3)
The slope of the given line is 8/3.
Since the line we want is parallel to the given line, it will have the same slope.
Now, we can use the point-slope form of a line to write the equation of the line passing through (-4, 7) with a slope of 8/3:
y - y1 = m(x - x1)
Substituting the values, we get:
y - 7 = (8/3)(x - (-4))
y - 7 = (8/3)(x + 4)
Multiplying through by 3 to eliminate the fraction, we get:
3y - 21 = 8(x + 4)
3y - 21 = 8x + 32
8x - 3y + 53 = 0