The equation of the line that goes through the point ( 3 ,5 ) and is parallel to the line 2 x + 4 y = 2 can be written in the form y = mx+b where m is and where b is?
Please help me !!!
where m is the slop and b is y.so the equation in given with 2x+4y=2 and the points that is given is (3,5) so what you have to do is to put in this form y=mx+b so 3 is x value and 5 is y value.we have the equation for that witch is y-y1=m(x-x1)
y-5=2(x-3)
y-5=2x-6
y+5=2x+5
when you add 5 to both sides it will give you y=2x-1
The slope of the line is -1/2:
2x + 4y = 2
4y = -2x + 2
y = -1/2 x + 1/2
To find the equation of a line parallel to the line 2x + 4y = 2 and passing through the point (3, 5), we need to determine the slope of the given line first.
Given line equation: 2x + 4y = 2
We can rewrite this equation in slope-intercept form (y = mx + b) by solving it for y:
4y = -2x + 2
y = (-2/4)x + 2/4
y = (-1/2)x + 1/2
The slope of the given line is -1/2.
Since the equation of the desired line is parallel to the given line, they have the same slope. Therefore, the slope (m) is also -1/2.
Now, we can use the point-slope form of a linear equation (y - y1 = m(x - x1)) to find the equation of the line passing through the point (3, 5):
y - 5 = (-1/2)(x - 3)
Simplifying further:
y - 5 = (-1/2)x + 3/2
y = (-1/2)x + 3/2 + 5
y = (-1/2)x + 3/2 + 10/2
y = (-1/2)x + 13/2
Therefore, the equation of the line that passes through the point (3, 5) and is parallel to the line 2x + 4y = 2 is y = (-1/2)x + 13/2.
In this equation, the value of m is -1/2, and the value of b is 13/2.
To find the equation of the line that is parallel to the line 2x + 4y = 2 and passes through the point (3, 5), you can follow these steps:
Step 1: Determine the slope (m) of the given line by rearranging the equation into slope-intercept form (y = mx + b). In this case, we have 2x + 4y = 2.
- Start by isolating y: 4y = -2x + 2.
- Divide both sides by 4: y = (-1/2)x + 1/2.
- The slope (m) of the line is -1/2.
Step 2: Since the line you are looking for is parallel to the given line, it will have the same slope. So, the slope of the line you are looking for is also -1/2.
Step 3: Now that you have the slope (m), you can use the point-slope form of a line to find the equation. The point-slope form is given as y - y1 = m(x - x1), where (x1, y1) is the given point (3, 5) and m is the slope (-1/2).
- Substituting the values, we get y - 5 = (-1/2)(x - 3).
Step 4: Finally, you can rearrange the equation into slope-intercept form (y = mx + b) by simplifying and isolating y.
- Distribute the -1/2 to the terms inside the parentheses: y - 5 = (-1/2)x + 3/2.
- Add 5 to both sides of the equation: y = (-1/2)x + 3/2 + 5.
- Simplify: y = (-1/2)x + 13/2.
Therefore, the equation of the line that passes through the point (3, 5) and is parallel to 2x + 4y = 2 can be written as y = (-1/2)x + 13/2, where m = -1/2 and b = 13/2.