Question

2 2 -2 Which of the following is an equation of line k in the xy-plane above? (A) y=-*-4 (B) y = x+2 (C) 2y - 3x = -8 (D) 2y - 3x = -4

Answer 1

Option C is correct.

The equation of line k is 2y - 3x = -8

Step-by-step explanation

The slope and y-intercept form of the equation of a straight line is given as

y = mx + c

where

y = y-coordinate of a point on the line.

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

c = y-intercept of the line.

From the graph attached, we can see that the y-intercept is -4 because the line crosses the y-axis at (0, -4).

Then, for the slope, for a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as

`Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=(y_2-y_1)/(x_2-x_1)`

Using the points where the graph crosses the x and y axis as the two points,

(x₁, y₁) and (x₂, y₂) are (0, -4) and (8/3, 0)

`\text{Slope = }(0-(-4))/((8)/(3)-0)=(4)/((8)/(3))=(3)/(2)`

Recall that

y = mx + c

m = 3/2

c = -4

y = (3/2) (x) - 4

Multiply through by 2

2y = 3x - 8

2y - 3x = -8

Hope this Helps!!!