## College Algebra (10th Edition)

The linear function is $f(x) = -3x+1$. Refer to the graph below.
RECALL: (1) The point-slope form of a line's equation is $y-y_1=m(x-x_1)$ where $(x_1, y_1)$ is a point on the line and $m$ = slope of the line. (2) The slope-intercept form of a line is $y=mx+b$ where $m$ = slope of the line and $b$ = y-intercept of the line. The line has: $m=-3$; contains the point $(-1, 4)$ Use the point-slope form in (1) above to obtain the line's equation: $y-4=-3[x-(-1)] \\y-4=-3(x+1)$ Isolate $y$ on one side to get the slope-intercept form of the line's equation: $y-4+4 = -3(x+1)+4 \\y=-3(x+1)+4 \\y=-3x-3+4 \\y=-3x+1$ Thus, the linear function is $f(x)=3x+1$ To graph the line, perform the following steps: (1) Plot the y-intercept point $(0 ,1)$. (2) Use the slope $-3$ or $\frac{-3}{1}$ to obtain another point on the line. From $(0, 1)$, move 3 units down (the rise) and 1 unit to the right (the run) t arrive at the point $(1, -2)$. (3) Connect the two points using a straight line to complete the graph. (refer to the image in the answer part above for the graph)