point-slope form: $y-5=6(x+2)$ slope-intercept form: $ y=6x+17$
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 $6$ and passes through the point $(-2, 5)$. Substitute these values into the point-slope form above to obtain: $y-5=6[x-(-2)] \\y-5 = 6(x+2)$ (b) slope-intercept form Substitute the slope 6 to $m$ to obtain the tentative equation: $y=6x+b$ The line passes through $(-2, 5)$. 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: $y=6x+b \\5 = 6(-2) + b \\5 = -12 + b \\5+12 = b \\17= b$ Thus, the equation of the line is $y=6x+17$.