Answer:
The point-slope form of the equation of the parallel line is y - 3 = [tex]\frac{3}{4}[/tex] (x - 4)
Step-by-step explanation:
Parallel lines have the same slopes and different y-intercepts
The slope-intercept form of the linear equation is y = m x + b, where
The point-slope form is of the linear equation is y - y1 = m(x - x1), where
∵ The equation of the given line is y = [tex]\frac{3}{4}[/tex] x - 3
→ Compare it with the first form of the equation above
∴ m = [tex]\frac{3}{4}[/tex]
∴ The slope of it is [tex]\frac{3}{4}[/tex]
∵ Parallel lines have the same slopes
∴ The slope of the parallel line is [tex]\frac{3}{4}[/tex]
∵ The point-slope form is y - y1 = m(x - x1)
→ Substitute the value of the slope in the form of the equation above
∴ y - y1 = [tex]\frac{3}{4}[/tex] (x - x1)
∵ The line passes through the point (4, 3)
∴ x1 = 4 and y1 = 3
→ Substitute them in the equation above
∴ y - 3 = [tex]\frac{3}{4}[/tex] (x - 4)
∴ The point-slope form of the equation of the parallel line is
y - 3 = [tex]\frac{3}{4}[/tex] (x - 4)
