point-slope form: $y+1=8(x-4)$ slope-intercept form: $y=8x-33$
Work Step by Step
RECALL: (1) The slope-intercept form of a line's equation is: $y=mx+b$ where m = slope and b = y-intercept (2) The point-slope form of a line's equation is: $y-y_1=m(x-x_1)$ (a) point-slope form The given line has a slope of $8$ and passes through the point $(4, -1)$. Substitute these values into the point-slope form above to obtain: $y-(-1)=8(x-4) \\y+1 = 8(x-4)$ (b) slope-intercept form Substitute the slope 8 to $m$ to obtain the tentative equation: $y=8x+b$ The line passes through $(4, -1)$. This means that the coordinates of this point satisfy the equation of the line. Substitute the x and y-coordinates of this point into the tentative equation to obtain: $y=8x+b \\-1 = 8(4) + b \\-1 = 32 + b \\-1-32 = b \\-33= b$ Thus, the equation of the line is $y=8x-33$.