Answer
Option Y is correct.
Explanation
We are told that the slope is multiplied by (1/2) and the y-intercept is increased by 3 units.
The original graph has a y-intercept (point where the graph crosses the y-axis) at point y = 1. Adding 3 units to that, changes the y-intercept to y = 4.
And that leaves options X and Y as viable answers.
But the original graph is positive sloping, and multiplying the slope by (1/2) only spreads the graph out more along the y-axis, it doesn't change the direction of the graph like option X has been changed to be negative sloping. This would only happen if the slope was multiplied by a negative number.
So, this leaves us with only Option Y as the viable answer.
And to be absolutely sure, we can go further and calculate the slope of the original graph and the graph in option Y.
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]For the original question,
(x₁, y₁) and (x₂, y₂) are (0, 1) and (-1, -1)
[tex]\text{Slope = }\frac{-1-1}{-1-0}=\frac{-2}{-1}=2[/tex]For the option Y,
(x₁, y₁) and (x₂, y₂) are (0, 4) and (-1, 3)
[tex]\text{Slope = }\frac{3-4}{-1-0}=\frac{-1}{-1}=1[/tex]1 is indeed half of 2. This confrims our answer.
Hope this Helps!!!
