(standard form MC)

Question

A graph of a linear relationship is shown.

Write an equation in standard form that models the relationship shown.



Answer 1

Generally, from my experience, standard form should be written with integers in the form Ax + By = C with the leading term (the x-term) having a positive coefficient (A).

Therefore, the equation derived correctly by the other experts using two different methods should be written with the equivalent equation as follows:

5x - y = 10

This can easily be done by applying the multiplication property of equality with a factor of -1 to each side of the equation.

This is just a nit-picky distinction, however.

Answer 2

The other equation that defines a line, besides slope-intercept form as Frank T. correctly mentioned, is point-slope form:

y - y₁ = m(x - x₁)

where m is the slope and (x₁,y₁) is any point that is on the line that is not the y-intercept.

It looks like the line passes through (2,0), so let's use that as our (x₁,y₁). Let's also use the slope Frank T. correctly calculated, 5.

Putting everything together:

y - 0 = 5(x - 2)

y = 5(x - 2)

Ax + By = C is standard form for a line

Expanding our point-slope equation of the line gives us:

y = 5x - 10

Rearranging to fit standard form:

-5x + y = -10

If the question asked for it, A = -5, B = 1, and C = -10

Hope this was helpful. Credits to Peter R. for catching a small multiplication error I made.

Answer 3

y=mx + b is the slope intercept form. m is the slope. B is the y-intercept, where the line crosses the y-axis.

This line crosses the y-axis at -10.

y = mx - 10

m is the slope = change in y / change in x. Pick two points (x,y), with the m = (y2 - y1)/(x2 - x1).

(0,-10) is one point, Point 1. (2,0) is point 2.

(0 - -10) / (2-0) = 10/2 = 5 is the slope.

y = 5x -10

Ax + By = c is standard form.

y = 5x -10

Subtract 5x from both sides.

y - 5x = -10