Final answer:
To find the equation of a line through (1, 8) and (-3, 4), calculate the slope (1) and use point-slope form to derive y = x + 7.
Step-by-step explanation:
To write the equation of a line that passes through the points (1, 8) and (-3, 4), you first need to find the slope of the line. The slope (m) can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the given points. Substituting the values from the points, we get m = (4 - 8) / (-3 - 1) = -4 / -4 = 1.
With the slope found, use the point-slope form of the line equation, y - y1 = m(x - x1), where (x1, y1) is either of the two points. Using the point (1, 8) and slope of 1, we get y - 8 = 1(x - 1). Simplifying this, we get the equation of the line: y = x + 7.
The final step is to write the equation in the slope-intercept form, which is y = mx + b. Here, m is the slope, and b is the y-intercept. Our equation is already in this form, indicating that the y-intercept is 7.