Final answer:
The equation of the line that passes through the points (1, 4) and (3, -4) is found by first calculating the slope (m = -4), and then using the slope-intercept form to find the y-intercept, resulting in the line equation y = -4x + 8.
Step-by-step explanation:
The student is asking how to find the equation of a line that passes through two points: (1, 4) and (3, -4). To find the equation of the line, we need to calculate the slope (m) and then use one of the points to find the y-intercept (b) using the slope-intercept form y = mx + b.
The slope is calculated by the difference in y-coordinates divided by the difference in x-coordinates:
m = (y2 - y1) / (x2 - x1) = (-4 - 4) / (3 - 1) = -8 / 2 = -4.
The slope of the line is -4.
Now, using the point (1, 4) and the slope -4, we can insert these values into the slope-intercept form:
y - y1 = m(x - x1)
y - 4 = -4(x - 1). To get y by itself, we expand and then isolate y:
y = -4x + 4 + 4
y = -4x + 8.
Therefore, the equation of the line is y = -4x + 8.