To find the slope and intercepts for the linear equation y = 3x + 8, we first need to identify the slope and how to calculate the y-intercept and x-intercept.
Slope
In the equation y = mx + b, m represents the slope. Here, the slope m is 3. This means that for every 1 unit increase in x, y increases by 3 units. The slope indicates how steep the line will be when graphed.
Y-Intercept
The y-intercept is found by setting x to 0. Substituting x = 0 into the equation gives:
y = 3(0) + 8 = 8Thus, the y-intercept is (0, 8). This is the point where the line crosses the y-axis.
X-Intercept
To find the x-intercept, we set y to 0 and solve for x:
0 = 3x + 8Solving for x gives:
3x = -8
x = -8/3So, the x-intercept is (-8/3, 0), which is the point where the line crosses the x-axis.
Graphing the Line
Now that we have both intercepts and the slope, we can graph the equation. Start by plotting the y-intercept (0, 8) on the graph. Then, from this point, use the slope to find another point; since the slope is 3, go up 3 units and then to the right 1 unit to plot the next point. Finally, draw a straight line through these points to represent the equation graphically.