graph the line with slope -2/3 passing through (-5, -5)
Slope is rise over run, so plot a point at (-5, -5) and go up 2, over to the right 3. Then from (-5, -5) go down 2 and left 3
easiest way:
since the slope is -2/3, the equation must look like this:
2x + 3y = C
plug in the point (-5,-5)
-10 - 15 = c = -25
2x + 3y = -25
re-arrange if needed.
Why did the line go to the party alone? Because it couldn't find a friend to slope with!
To graph the line with a slope of -2/3 passing through the point (-5, -5), follow these steps:
Step 1: Start by plotting the given point (-5, -5) on a coordinate plane. This point will be on the line we are trying to graph.
Step 2: Remember that the slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept. Since we have the slope (-2/3), we can write the equation for the line as y = (-2/3)x + b.
Step 3: To find the y-intercept (b), substitute the coordinates of the given point (-5, -5) into the equation. So, we have -5 = (-2/3)(-5) + b. Simplifying this equation, we get -5 = 10/3 + b.
Step 4: Solve for b by isolating it. Subtract 10/3 from both sides of the equation: -5 - 10/3 = b. To simplify this, multiply -5 by 3/3 to get -15/3. Therefore, b = -15/3 - 10/3, which equals -25/3.
Step 5: Now that we have both the slope (-2/3) and the y-intercept (-25/3), we can write the equation for the line as y = (-2/3)x - 25/3.
Step 6: Use the equation to plot additional points on the line. For example, pick a convenient x-value, substitute it into the equation, and solve for y. Repeat this process to generate at least one more point on the line.
Step 7: Once you have at least two points on the line, draw a straight line connecting them. This line represents the graph of the equation y = (-2/3)x - 25/3.
So, using these steps, you can now graph the line with a slope of -2/3 passing through the point (-5, -5) on a coordinate plane.
y + 5 = -2/3 x -10/3
y = -2/3 x -10/3-5
y = -2/3 x -25/3