Graph: 2x + 1.5y = -60 and 2x + y = -50
Answer (1)
To solve the given linear equations and graph them, we'll follow these steps:
Step 1: Understand the Equations
We have two linear equations:
2 x + 1.5 y = − 60
2 x + y = − 50
These are linear equations in two variables, "x" and "y".
Step 2: Convert to Slope-Intercept Form
The slope-intercept form of a line is y = m x + b , where m is the slope and b is the y-intercept.
First Equation:
From 2 x + 1.5 y = − 60 , solve for y :
\[1.5y = -60 - 2x\]
\[y = \frac{-60 - 2x}{1.5}\]
Simplifying, divide each term by 1.5:
\[y = -\frac{40}{3} - \frac{4}{3}x\]
Second Equation:
From 2 x + y = − 50 , solve for y :
\[y = -50 - 2x\]
Step 3: Graph the Equations
Equation 1: y = − 3 4 x − 3 40
This line has a slope of − 3 4 and a y-intercept of − 3 40 .
Equation 2: y = − 2 x − 50
This line has a slope of − 2 and a y-intercept of − 50 .
How to Graph:
Start by plotting the y-intercept for each line on the y-axis. For equation 1, plot − 3 40 , and for equation 2, plot − 50 .
Use the slope to determine the direction and steepness of each line. From the y-intercept, for equation 1, move down 4 units and right 3 units to plot another point. For equation 2, move down 2 units and right 1 unit to plot another point.
Draw straight lines through the points plotted for each equation to complete the graph.
Step 4: Find Intersection (If Needed)
If you need to find the point of intersection, you can set the equations equal as they both represent y and solve for x , then back-solve for y to find the intersection point.
These steps will help visualize the solution to the system of equations by graphing them.
