Final answer:
The equation of the line with a slope of 3 that passes through the point (7, -78) is y = 3x - 99. To find this, we plug in the slope and the point's coordinates into the slope-intercept form equation and solve for the y-intercept.
Step-by-step explanation:
To write the equation of a line with a slope of 3 that passes through the point (7, -78), we can use the slope-intercept form of a line, which is y = mx + b. Here, m represents the slope, and b represents the y-intercept. Since we know the slope (m) is 3, we can substitute this value into our equation, which gives us y = 3x + b.
To find the value of b, the y-intercept, we use the coordinates of the given point that the line passes through. Plugging in the values from the point (7, -78) into the equation gives us -78 = 3(7) + b. We then solve for b by performing the algebraic operations:
-78 = 21 + b
b = -78 - 21
b = -99
Now that we have both the slope and the y-intercept, we can write the final equation of the line in slope-intercept form: y = 3x - 99.