Final answer:
The Graphing linear functions is a straight line. The y-intercept and the slope of the line determine its characteristics. We can graph the given equations by identifying the y-intercept and slope, and then plotting the points and connecting them.
Step-by-step explanation:
The graph of the linear function can be described by the equation y = a + bx. The letter a represents the y-intercept, which is the point where the line crosses the y-axis. The letter b represents the slope of the line, which determines the steepness of the line. If b > 0, the line slopes upward to the right. If b = 0, the line is horizontal. If b < 0, the line slopes downward to the right.
Now let's graph the given equations:
a) y + 2 = -3(x - 4): The equation is in point-slope form. We can rearrange it to y = -3x + 14 which is in slope-intercept form. The y-intercept is (0, 14) and the slope is -3. We can plot these points and draw a straight line passing through them.
b) y + 4 = 2(x + 3): Rearranging the equation to slope-intercept form gives us y = 2x - 2. The y-intercept is (0, -2) and the slope is 2. Plotting the y-intercept and using the slope, we can graph the line.
c) y - 3 = x + 5: By rearranging, we get y = x + 8. The y-intercept is (0, 8) and the slope is 1. The line can be graphed using these coordinates.
d) y = -(x - 2): The equation is already in slope-intercept form as y = -x + 2. The y-intercept is (0, 2), and the slope is -1. Plotting the points and connecting them gives us the graph of the linear function.