Let's learn how to graph the linear equation y equals 5x plus 4. This equation is in slope-intercept form, where m equals 5 is the slope and b equals 4 is the y-intercept. We'll use these values to plot points and draw our line.
The first step is to plot the y-intercept. The y-intercept is where the line crosses the y-axis, which happens when x equals zero. Substituting x equals zero into our equation y equals 5x plus 4, we get y equals 5 times zero plus 4, which equals 4. So our y-intercept is at the point zero comma 4.
Now we use the slope to find a second point. The slope is 5, which we can write as 5 over 1, meaning rise over run. Starting from our y-intercept at zero comma 4, we move right 1 unit for the run, then up 5 units for the rise. This brings us to the point 1 comma 9.
Finally, we draw a straight line through our two points: zero comma 4 and 1 comma 9. This line represents all solutions to the equation y equals 5x plus 4. We extend the line in both directions with arrows to show that it continues infinitely. Our graph is now complete, showing the linear relationship between x and y.
To summarize what we've learned: The linear equation y equals 5x plus 4 has a slope of 5 and y-intercept of 4. We plot the y-intercept at zero comma 4, use the slope to find a second point at 1 comma 9, then draw a straight line through both points. This complete graph represents all solutions to our linear equation.