Answer:
y = -6/5x - 2
Step-by-step explanation:
Parallel lines have the same slopes. Given the point, (-5, 4), and the linear equation, y = -6/5x + 2 (where the slope, m = -6/5), we can assume that the other line will have the same slope = -6/5. All we need to do at this point is determine the y-intercept, b, of the other line.
The y-coordinate (b) of the point, (0, b) is the y-intercept of the line where the graph of the linear equation crosses the y-axis. The y-intercept is also the value of y when x = 0.
Using the slope, m = -6/5, and the given point, (-5, 4), substitute these values into the slope-intercept form to solve for b:
y = mx + b
4 = -6/5(-5) + b
4 = 6 + b
Subtract 6 from both sides to isolate b:
4 - 6 = 6 - 6 + b
-2 = b
Therefore, the y-coordinate value of the y-intercept, (0, -2) is b = -2.
The linear equation of the line parallel to y = -6/5x + 2 is:
y = -6/5x - 2 (please take note of the negative value of the y-intercept in the final answer. It is different from the given equation).
Attached is a screenshot of the graphed equations, where it shows the parallel lines with different y-intercepts.
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