Answer:
The equation of the line parallel to 2y = x – 3 and passing through point (-4,3) in slope-intercept form is y = (1/2)x + 5.
Explanation:
To find the equation of a line that is parallel to 2y = x – 3, we need to determine the slope of the given line.
2y = x - 3 can be written in slope-intercept form y = (1/2)x - 3/2.
The slope of this line is 1/2.
Since we want a line parallel to this line, the slope of the new line will also be 1/2.
Next, we can use the point-slope form of a line to write the equation of the new line.
Point-slope form: y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope of the line.
Substituting the values, we get:
y - 3 = (1/2)(x - (-4))
Simplifying, we get:
y - 3 = (1/2)x + 2
Adding 3 to both sides, we get the final equation in slope-intercept form:
y = (1/2)x + 5
Therefore, the equation of the line parallel to 2y = x – 3 and passing through point (-4,3) in slope-intercept form is y = (1/2)x + 5.