Final answer:
Using the slope-intercept form y = mx + b, we can substitute the given slope of 5 and the point (2, 10) into the equation and solve for the y-intercept b, resulting in the final equation of y = 5x with a y-intercept of 0.
Step-by-step explanation:
To find the equation of a line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept, we can use the given point (2, 10) and the slope of 5. The slope represents the rise over run, meaning for every unit increase in x, the y value increases by the slope.
Let's start by using the slope-intercept form:
y = mx + b
We know the slope (m) is 5, so we can plug that in:
y = 5x + b
Now, we need to find the y-intercept (b). We can substitute the x and y from the point (2, 10) into the equation and solve for b:
10 = 5(2) + b
10 = 10 + b
b = 10 - 10
b = 0
Now we have the y-intercept, so the final equation is:
y = 5x