Final answer:
The equation of the line with a slope of 15 that contains the point (10, 5) is y = 15x - 145, found by substituting the slope and point into the point-slope form and then rearranging into slope-intercept form.
Step-by-step explanation:
To find the equation of a line with a given slope m=15 that passes through a specific point (10,5), you can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
Substituting the given point (10,5) and the slope (15) into the equation, we get:
y - 5 = 15(x - 10)
To put this into the slope-intercept form (y = mx + b), we first distribute the slope through the parenthesis and then isolate y:
y - 5 = 15x - 150
Adding 5 to both sides to solve for y:
y = 15x - 145
This is the equation of the line in slope-intercept form, with m as the slope and -145 as the y-intercept.