write an equation of the line containing the given point and parallel to the given line
(3,-3) 7x-2y=5
need help please
7(3)-2(-3)= 5 ?
21- 6= 5? this does not look right, please show me where I am supposed to place the (3,-3)to solve the equation thanks
First find the slope of the given line (7x - 2y = 5). Then use y - y1 = m(x - x1) to find the equation of the line passing through the point (x1, y1) = (3, -3)
-5,4?
y2-y1
-----
x2-x1
2-(-3)
------ -5/4
7-3
How do you find the slope of a line? If the point were changed to (1, 1) would the slope of the line change?
If y = mx + b, then the slope is m and the y-intercept is b.
To write the equation of a line parallel to the given line and passing through the given point, you need to follow these steps:
1. Find the slope of the given line. The equation of the given line is in the form: Ax + By = C. Rearrange it to isolate y and write the equation in slope-intercept form (y = mx + b), where m is the slope.
Given equation: 7x - 2y = 5
Rearrange: -2y = -7x + 5
Divide by -2: y = 7/2x - 5/2
So, the slope of the given line is m = 7/2.
2. Since the line you want to write the equation for is parallel to the given line, it will have the same slope as the given line.
3. Use the point-slope form of a linear equation (y - y1 = m(x - x1)), where (x1, y1) is the given point (3, -3) and m is the slope (7/2), to find the equation of the line:
y - (-3) = (7/2)(x - 3)
y + 3 = (7/2)(x - 3)
4. Simplify the equation:
y + 3 = (7/2)x - (7/2) * 3
y + 3 = (7/2)x - 21/2
5. Finally, if needed, rearrange the equation into a standard form. Multiply every term by 2 to remove fractions:
2y + 6 = 7x - 21
7x - 2y = 27
Therefore, the equation of the line parallel to the given line and passing through the point (3, -3) is 7x - 2y = 27.