point-slope form: $y-5=2(x-3)$ slope-intercept form: $y = 2x -1$
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 $2$ and passes through the point $(3, 5)$. Substitute these values into the point-slope form above to obtain: $y-5=2(x-3)$ (b) slope-intercept form Substitute the slope 2 to $m$ to obtain the tentative equation: $y=2x+b$ The line passes through $(3, 5)$. 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: $y=2x=b \\5 = 2(3) + b \\5 = 6 + b \\5-6 = b \\-1 = b$ Thus, the equation of the line is $y=2x-1$.