To write an equation for the line parallel to the given line described by the equation y = 5x + 4 and that passes through the point (c, 38), we first need to identify the slope of the given line.
The equation y = 5x + 4 is in slope-intercept form, which is y = mx + b, where m represents the slope. So, the slope of the given line is 5.
Since parallel lines share the same slope, the slope of our new line will also be 5.
Next, we can use the point-slope form to find the equation of the line that passes through the point (c, 38). The point-slope form is given by:
y – y1 = m(x – x1)
Substituting in our point (c, 38) and the slope 5, we can express the equation as:
y – 38 = 5(x – c)
To convert this into slope-intercept form, we first simplify:
y – 38 = 5x – 5c
Then, add 38 to both sides:
y = 5x – 5c + 38
So, the equation of the line parallel to y = 5x + 4 that contains the point (c, 38) is:
y = 5x – 5c + 38