The graph represents a line with a slope of -2/3 and a y-intercept equal to that of the line y = 2/3x – 2 is A coordinate plane with a line passing through (negative 3, 0) and (0, negative 2).
What is slope?
The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx.
What are intercepts?
Using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. As such, these points satisfy x = 0.
According to the question
Represents a line with a slope of -2/3
i.e ,
m = -2/3
y-intercept equal to that of the line
y = [tex]\frac{2}{3}x-2[/tex]
i.e ,
at y-intercept , x = 0
y = -2
Now, Putting value in standard form of line
y = mx + c
-2 = 0 + c
c = -2
now , substituting the values of m and c in standard form of line
y = mx + c
y = [tex]\frac{-2}{3}x-2[/tex] --------- (equation of graph )
Now ,
x y
0 -2
3/2 1
3 0
Only option 4 have these points
Hence, The graph represents a line with a slope of -2/3 and a y-intercept equal to that of the line y = 2/3x – 2 is A coordinate plane with a line passing through (negative 3, 0) and (0, negative 2).
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