Question

Which equations and/or functions represent the graphed line? Select three options. A coordinate plane with a line passing through the points, (negative 4, 0), (negative 2, 1), (0, 2), and (2, 3).

Answer 1

Answer:

Option:-Point slope form : y-3=\frac{1}{2}(x-2)

Slope intercept form: y=\frac{1}{2}(x)+2

Standard form : -x+2y=4

Step-by-step explanation:

From the given graph it is clear that the line is passing through the points, (-4, 0), (-2, 1), (0, 2), and (2, 3).

If a line passes through two points (x_1,y_1) and (x_2,y_2), then the equation of line is

y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)

Let as consider any two points of the line: (2, 3) and (0, 2).

The equation of line is

y-3=\frac{2-3}{0-2}(x-2)

y-3=\frac{1}{2}(x-2)

The point slope form of the line is y-3=\frac{1}{2}(x-2).

y-3=\frac{1}{2}(x)-\frac{1}{2}(2)

y-3=\frac{1}{2}(x)-1

Add 3 on both sides.

y=\frac{1}{2}(x)-1+3

y=\frac{1}{2}(x)+2

Therefore the slope intercept form of the line is y=\frac{1}{2}(x)+2.

Multiply both sides by 2.

2y=x+4

-x+2y=4

Therefore, the standard form of the line is -x+2y=4.

Explanation:

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