Final answer:
To find the equation of a line that is parallel to y = ⅓x + ⅛ and passes through (-1,4), we use the point-slope form with the same slope ⅓. After calculation, the resultant equation is y = ⅓x + ⅞.
Step-by-step explanation:
The student has asked how to find the equation of a line that passes through the point (-1,4) and is parallel to another line given by the equation y = ⅓x + ⅛. To find the equation of this line, we'll use the concept that parallel lines have the same slope. The slope of the given line is ⅓. Therefore, the slope of the line we want to find is also ⅓.
Next, we use the point-slope form of the equation of a line, which is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line. Substituting the given point (-1,4) and the slope ⅓, the equation of the line becomes y - 4 = ⅓(x + 1).
To put this equation in the slope-intercept form, we distribute the slope on the right side and add 4 to both sides, which gives us y = ⅓x + ⅓ + 4. Simplifying further we get y = ⅓x + ⅛ + 4, and finally, y = ⅓x + ⅞, which is the equation of the line that the student is seeking.