point-slope form: $y-3 = 4(x-1)$ slope-intercept form: $y=4x-1$
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 $4$ and passes through the point $(1, 3)$. Substitute these values into the point-slope form above to obtain: $y-3=4(x-1)$ (b) slope-intercept form Substitute the slope 4 to $m$ to obtain the tentative equation: $y=4x+b$ The line passes through $(1, 3)$. 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: $y=4x+b \\3 = 4(1) + b \\3 = 4 + b \\3-4 = b \\-1 = b$ Thus, the equation of the line is $y=4x-1$.