We are given the equation of the following line:
[tex]y=-\frac{2}{3}x+1[/tex]
This equation is of the form:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept. If the slope of a line is negative, it means that the y-values will decrease as the x-values increase, in other words, the graph will go downwards. The y-intercept indicates where the graph will touch the y-axis, in this case, that value is 1, therefore, the graph must intercept the y-axis at 1.
The options that meet these conditions are A and B. to determine which is the correct one we need to find the intercept with the x-axis, to do that we will set the value of y to zero and we'll solve for "x", like this:
[tex]0=-\frac{2}{3}x+1[/tex]
Now we subtract 1 to both sides:
[tex]-1=-\frac{2}{3}x[/tex]
Now we multiply both sides by 3:
[tex]-3=-2x[/tex]
Now we divide by -2:
[tex]\begin{gathered} \frac{3}{2}=x \\ 1.5=x \end{gathered}[/tex]
Therefore, the graph must intercept the x-axis at x = 1.5. The graph that meets all of these conditions is option A.
