The parallel line to y = [tex]\frac{3}{2}[/tex] x + 3 and passes through
the point (0 , 4) is y = [tex]\frac{3}{2}[/tex] x + 4
Step-by-step explanation:
Parallel lines have:
1. The same slopes
2. The different y-intercept
The slope-intercept form of the linear equation is y = m x + c, where
m is the slope of the line and c is the y-intercept
We need to find the equation of the line that is parallel to
y = [tex]\frac{3}{2}[/tex] x + 3 and passes through the point (0 , 4)
∵ The two lines are parallel
∴ Their slopes are equal
∵ The equation of the given line is y = [tex]\frac{3}{2}[/tex] x + 3
∵ The form of the equation is y = m x + c
∴ m = [tex]\frac{3}{2}[/tex]
∴ The slope of the line is [tex]\frac{3}{2}[/tex]
∵ The equation of the line is y = mx + c
∵ m = [tex]\frac{3}{2}[/tex]
∴ The equation of the line is y = [tex]\frac{3}{2}[/tex] x + c
- To find c substitute x and y in the equation by the coordinates of
a point lies on the line
∵ The line passes through the point (0 , 4)
∴ x = 0 , y = 4
∴ 4 = [tex]\frac{3}{2}[/tex] (0) + c
∴ c = 4
∴ The equation of the line is y = [tex]\frac{3}{2}[/tex] x + 4
The parallel line to y = [tex]\frac{3}{2}[/tex] x + 3 and passes through
the point (0 , 4) is y = [tex]\frac{3}{2}[/tex] x + 4
Learn more:
You can learn more about equations of parallel lines in brainly.com/question/8628615
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