Answer
Option C is correct.
The equation of line k is 2y - 3x = -8
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
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]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)
[tex]\text{Slope = }\frac{0-(-4)}{\frac{8}{3}-0}=\frac{4}{\frac{8}{3}}=\frac{3}{2}[/tex]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!!!
