Question

Write the standard form of the equation through: (-5, 4), parallel to y=-6/5x + 2

Answer 1

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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