Since the x-intercept is 1, then another point on the graph of the function is (1,0).
Use the slope formula to find the slope of the line that passes through the points (1,0) and (-2,6):
[tex]\begin{gathered} m=\frac{6-0}{-2-1} \\ =\frac{6}{-3} \\ =-2 \end{gathered}[/tex]
Use the point-slope formula. Substitute y₁=6, x₁=-2 and m=-2. Then, isolate y to find the equation in sope-intercept form:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \Rightarrow y-6=-2(x-(-2)) \\ \Rightarrow y-6=-2(x+2) \\ \Rightarrow y-6=-2x-4 \\ \Rightarrow y=-2x-4+6 \\ \Rightarrow y=-2x+2 \end{gathered}[/tex]
Therefore, the answer is:
[tex]y=-2x+2[/tex]
