Finding the Equation of a Parallel Line
To find the equation of a line that is parallel to a given line, you need to determine two key components: the slope of the given line and the point through which the new line passes.
Step 1: Identify the Slope
The provided line is given by the equation:
y = 5x + 4
From this equation, it’s clear that the slope (m) is 5. Lines that are parallel share the same slope, so the slope of our new line will also be:
m = 5
Step 2: Use the Point-Form Equation
Next, we know our parallel line passes through the point (c, 38). To find the equation of our line, we can use the slope-intercept form:
y = mx + b
We need to find the y-intercept (b). We can substitute the slope and the coordinates of the point (c, 38) into the equation:
38 = 5c + b
Step 3: Express b in terms of c
To isolate b, rearranging the equation gives us:
b = 38 – 5c
Step 4: Write the Final Equation
Now we can place the slope and the value of b back into the slope-intercept form:
y = 5x + (38 – 5c)
This can be simplified slightly, but in this case, it’s optimal to leave it in this form for clarity. This is the equation of the line parallel to the original line that passes through the point (c, 38).