Sohini H. answered • 01/20/21
Top Medical Student and Experienced Tutor in Chemistry and Writing
First, let's find the x and y intercepts. An intercept is when the line we graph crosses, or intercepts, either the x or y axis. To find the x-intercept, we need to know what the x-value will be when y=0. Conversely, we will find the y-intercept when we know what the y-value will be when x=0. Let's plug these in.
If x=0 in 3x+5y=15, then the equation becomes 0+5y=15. y=3, so y=3 is our y-intercept.
If y=0 in 3x+5y=15, then the equation becomes 3x+0=15. x=5, so x=5 is our x-intercept.
To graph the equation, we now have everything we need. We have two points, (5,0) and (0,3), our intercepts. Plot your intercepts and connect the line between the points.
In addition, we can also solve this by finding the slope. Let's convert the equation to the y=mx + b format.
3x + 5y = 15
5y = -3x + 15
y = (-3/5)x + 3
m=(-3/5), which we know is our slope. Notice that b=3, which confirms our y=intercept is in fact y=3, or (0,3). Using this method, if you plot (0,3), and then go 3 units down and 5 units to the right, you will find your next point.
You can always graph a line if you have either two points, like we did in the first method, or one point and the slope, like we did in the second method.
