Answer:
y = -5/4x + 12
Explanation:
Step 1: Find the slope of 5x + 4y = 8
Parallel lines have the same slopes. Thus, we first need to find the slope of 5x + 4y = 8, which is currently in standard form, whose general equation is:
Ax + By = C.
We can find the slope by converting from standard to slope-intercept form, whose general equation is:
y = mx + b, where
- m is the slope,
- and b is the y-intercept:
5x + 4y = 8
Subtracting 5x from both sides gives us:
4y = -5x + 8
Dividing both sides by 4 gives us:
y = -5/4x + 2
Thus, the slope of 5x + 4y = 8 is -5/4. This means that the slope of the line we're trying to find is also -5/4.
Step 2: Plug in (8, 2) for x and y and -5/4 for m in the slope-intercept form to find b, the y-intercept:
2 = -5/4(8) + b
2 = -10 + b
12 = b
Thus, y = -5/4x + 12 is the equation of the line in slope-intercept form that contains that point (8, 2) and is parallel to the line 5x + 4y = 8