Question

Find the equation of a straight line which is parallel to 2y = x-3 and passes through (3, -2)​

Answer 1

y = (1/2)x - 3.5

Explanation:

Straight lines that are parallel to each other will have the same slope. If the reference line is 2y = x- 3, we can rewrite it in standard slope-intercept form of y = mx + b, where m is the slope and b is the y-intercept.

2y = x- 3

y = (1/2)x- (3/2)

Since the reference line has slope of (1/2), a parallel line will also have a slope of (1/2). Lets write what we can of the new line:

y = (1/2)x + b

Any value of b will result in a parallel line. But we need a value that will shift the line so that it intersect the point (3,-2) [passes through it]. This can be done by entering that point into the equation we have thus far and solve for b:

y = (1/2)x + b

-2 = (1/2)(3) + b [For point (3,-2)]

-2 = 1.5 + b

b = - 3.5

The equation of the parallel line that passes through point (3,-2) is:

y = (1/2)x - 3.5

See the attached graph.

Answer 2

To find the equation of a straight line that is parallel to the line 2y = x - 3, we need to determine the slope of the given line. The slope-intercept form of a line is y = mx + b, where m represents the slope.

Let's rewrite the given line 2y = x - 3 in slope-intercept form:

2y = x - 3
y = (1/2)x - 3/2

From this form, we can see that the slope of the given line is 1/2.

Since the line we're trying to find is parallel to this line, it will have the same slope. Now we can use the point-slope form of a line to find the equation, using the given point (3, -2):

y - y₁ = m(x - x₁)

Plugging in the values, we have:

y - (-2) = (1/2)(x - 3)
y + 2 = (1/2)(x - 3)
2y + 4 = x - 3
x - 2y = 7

Therefore, the equation of the straight line that is parallel to 2y = x - 3 and passes through the point (3, -2) is x - 2y = 7.