Final answer:
To write the equation of a line passing through (-1, 1) parallel to y = -3/4x - 5, we use the same slope of -3/4. By substituting the point into the slope-intercept form and solving for the y-intercept, we find the y-intercept to be 1/4, yielding the equation y = -3/4x + 1/4.
Step-by-step explanation:
The slope-intercept form of the equation of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept. To write the equation of a line that passes through the point (-1, 1) and is parallel to the line described by y = -3/4x - 5, we need to use the same slope since parallel lines have equal slopes. Hence, the slope m will be -3/4. To find the y-intercept b, we use the given point and the slope in the slope-intercept form:
y - y1 = m(x - x1)
Here, (x1, y1) is the point (-1, 1). Plugging these values in gives:
1 = (-3/4)(-1) + b
By solving for b, we get:
b = 1 - 3/4
b = 1/4
Therefore, the equation of the line is y = -3/4x + 1/4.