The given equation is y + 2 = 4(x - 1)
The equation of the parallel line in the slope-intercept form is y = 4x - 7
Step-by-step explanation:
Parallel lines have
- Same slopes
- Different y-intercepts
The slope-intercept form of the equation of a line is y = mx + b, where m is the slope of the line and b is the y-intercept
∵ The equation of the given line is y + 2 = 4(x - 1)
- Change its form to slope-intercept form to find its slope
∵ y + 2 = 4(x) - 4(1)
∴ y + 2 = 4x - 4
- Subtract 2 from both sides
∴ y = 4x - 6
- Compare it with the slope-intercept form to find m
∵ the slope-intercept form is y = mx + b
∴ m = 4
∵ The parallel lines have same slopes
∴ The slope of the parallel line is 4
- Substitute it in the form of the equation
∴ The equation of the parallel line is y = 4x + b
- To find b substitute x and y in the equation by the
coordinates of a point on the line
∵ The parallel line passes through point (1 , -3)
∴ x = 1 and y = -3
∵ -3 = 4(1) + b
∴ -3 = 4 + b
- Subtract 4 from both sides
∴ -7 = b
∴ The equation of the parallel line is y = 4x + (-7)
∴ The equation of the parallel line is y = 4x - 7
The equation of the parallel line in the slope-intercept form is y = 4x - 7
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