Final answer:
To write the given equations in slope-intercept form, distribute the coefficient of 'x' on the right-hand side, then solve for 'y' to get y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
Step-by-step explanation:
The subject of this question is Mathematics, specifically dealing with equations of straight lines.
Slope-Intercept Form of an Equation
For the equation y - 3 = -5(x + 12), we want to convert it into slope-intercept form, which is y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
First, distribute the -5:
y - 3 = -5x - 60
Then, add 3 to both sides:
y = -5x - 57
For the equation y - 2/3 = -2(x - 1/4), distribute the -2:
y - 2/3 = -2x + 1/2
To get y alone, add 2/3 to both sides:
y = -2x + 1/2 + 2/3
Combine like terms to get the final slope-intercept form:
y = -2x + 7/6