Answer:
To find the equation of a line that is parallel to the line -8x + 4y = 24 and passes through the point (12, 16), we need to follow these steps:
Step 1: Determine the slope of the given line
To find the slope of the given line -8x + 4y = 24, we need to rewrite it in slope-intercept form, which is y = mx + b, where m represents the slope.
So, let's rearrange the equation:
-8x + 4y = 24
4y = 8x + 24
y = 2x + 6
The slope of the given line is 2.
Step 2: Use the slope and the given point to find the equation of the parallel line
Since the parallel line has the same slope as the given line, which is 2, we can use the point-slope form of a line to find its equation. The point-slope form is given by: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.
Let's plug in the values:
(x₁, y₁) = (12, 16)
m = 2
The equation becomes:
y - 16 = 2(x - 12)
Now, simplify:
y - 16 = 2x - 24
To convert it to the slope-intercept form, isolate y:
y = 2x - 8
Therefore, the equation of the line that passes through (12, 16) and is parallel to -8x + 4y = 24 in point-slope form is:
y - 16 = 2(x - 12)
Explanation: