Final answer:
The equation of the line with a slope of 8 that passes through the point (1,3) is y = 8x - 5.
Step-by-step explanation:
The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept. Given a slope of 8 and a point through which the line passes, namely (1,3), we can use these to find the equation of the line. To write the equation of a line in slope-intercept form (y = mx + b), we need the slope (m) and the y-intercept (b). We are given the slope (8) and the point (1,3) that the line passes through. To find the y-intercept, we use the point-slope formula: y - y1 = m(x - x1), where (x1, y1) is the given point.
First, we substitute the known slope (m = 8) and the coordinates of the given point into the slope-intercept form to find the y-intercept (b). So we have:
y = mx + b
3 = 8(1) + b
3 = 8 + b
b = 3 - 8
b = -5
Now, with b = -5, the equation of the line is y = 8x - 5.