parallel to 3x - 4y + 4 = 0 with the same x-intercept as y = 1/2 x -4
To find a line parallel to the line 3x - 4y + 4 = 0, we need to use the fact that parallel lines have the same slope.
First, let's rewrite the given line in slope-intercept form (y = mx + b):
3x - 4y + 4 = 0
-4y = -3x - 4
y = (3/4)x + 1
Since the given line has a slope of 3/4, any line parallel to it will also have a slope of 3/4.
Now, let's find the x-intercept of the line y = (1/2)x - 4. The x-intercept occurs when y = 0:
0 = (1/2)x - 4
(1/2)x = 4
x = 8
Therefore, the x-intercept of the line y = (1/2)x - 4 is x = 8.
To find the equation of the line parallel to 3x - 4y + 4 = 0 with the same x-intercept, we can use the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is a point on the line.
We know that the desired line has a slope of 3/4 and an x-intercept of 8. So, let's use the point (8, 0):
y - 0 = (3/4)(x - 8)
y = (3/4)x - 6
Therefore, the equation of the line parallel to 3x - 4y + 4 = 0 with the same x-intercept as y = (1/2)x - 4 is y = (3/4)x - 6.
To find a line parallel to 3x - 4y + 4 = 0, we need to determine the slope of the given line. We can rewrite the equation in slope-intercept form (y = mx + b), where m represents the slope:
3x - 4y + 4 = 0
-4y = -3x - 4
y = (3/4)x + 1
From this equation, we can see that the slope of the given line is 3/4.
To find a line parallel to this, we need to use the same slope of 3/4. We are also given that the line should have the same x-intercept as y = (1/2)x - 4.
The x-intercept of a line occurs when y is equal to zero. So, we can substitute zero for y in the equation y = (1/2)x - 4 and solve for x.
0 = (1/2)x - 4
(1/2)x = 4
x = 8
Hence, the x-intercept of y = (1/2)x - 4 is x = 8.
Now, we can use the slope (3/4) and the x-intercept (8) to get the equation of the line parallel to 3x - 4y + 4 = 0 and having the same x-intercept as y = (1/2)x - 4.
Using the slope-intercept form (y = mx + b), we can plug in the values we have:
y = (3/4)x + b
To find the value of b, we substitute the coordinates of the x-intercept (8, 0) into the equation:
0 = (3/4)(8) + b
0 = 6 + b
b = -6
Thus, the equation of the line parallel to 3x - 4y + 4 = 0 with the same x-intercept as y = (1/2)x - 4 is:
y = (3/4)x - 6.
y = 1/2 x - 4 has x-intercept at (8,0)
3x - 4y + 4 = 0 has slope 3/4
so, your line is (using point-slope form)
(y-0) = (3/4)(x-8)