Final answer:
The equation in slope-intercept form for the line with a slope of 3 and a y-intercept at -4 is y = 3x - 4.
Step-by-step explanation:
To write an equation in slope-intercept form for a line with a slope of 3 and a y-intercept at −4, use the formula y = mx + b, where 'm' is the slope and 'b' is the y-intercept. The given slope is 3, which means for every unit increase in x, y increases by 3 units. The y-intercept is given as −4, indicating that the line crosses the y-axis at -4. Therefore, by substituting 'm' with 3 and 'b' with -4, the equation in slope-intercept form becomes:
y = 3x − 4
Remember that the y-intercept of a line is the value of y at the point where the line crosses the y-axis (the x-coordinate is 0 at that point).