Write an equation of a line in slope-intercept form for the given conditions.
passes through (4,33) and (1,21)

The desired equation is thus   y = 4x + 17

Step-by-step explanation:

The slope-intercept form of the equation of a straight line is y = mx + b.  There are two values to find:  slope m and y-intercept b.

The line passes through (4, 33).  Thus, 33 = m(4) + b.

The line also passes through (1, 21).  Thus, 21 = m(1) + b, or m = 21 - b.

Thus we have a system of linear equations to solve, and will use the substitution method:

Substitute 21 - b for m in 33 = 4m + b:

33 = 4(21 - b) + b, which, in expanded form, is 33 = 84 - 4b + b, or

                                                                             33 = 84 - 3b, of

                                                                             -51 = -3b.

Thus, b = 17.  Since m = 21 - b, when b = 17, m = 21 - 17 = 4

The desired equation is thus   y = 4x + 17

Of course there are other ways to find this equation.  You could, if you wished, find the slope of the line passing through the given points using the definition of slope, and then find the y-intercept.

at first, in 1635, the evening meetings had been just for women . .

what relationship between ideas is shown in the text above?

question 1 options:

location of events

similarity of events

timing of events

examples of an idea

step-by-step explanation:

6e14 is the answer.