Graph the line with slope - 2 passing through the point (4, - 3).
We know that the slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. We also know that the line has a slope of -2 and passes through the point (4, -3).
To find the equation of the line, we can plug in the values of m and x and y for the point we know:
-3 = (-2)(4) + b
-3 = -8 + b
b = 5
So the equation of the line is y = -2x + 5.
To graph the line, we can plot the y-intercept (0, 5) and then use the slope to find additional points. We can start at the y-intercept and move down 2 units and right 1 unit to get the point (1, 3). We can repeat this process to get additional points (-1, 7), (2, 1), and so on.
Alternatively, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
We can plug in the values we know:
y - (-3) = -2(x - 4)
y + 3 = -2x + 8
y = -2x + 5
This is the same equation we found before.
To graph the line with a slope of -2 passing through the point (4, -3), follow these steps:
Step 1: Plot the given point on the coordinate plane. Start by marking a point at (4, -3) on the graph.
Step 2: Use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept, to determine the equation of the line. Since the slope is -2, the equation will be y = -2x + b.
Step 3: Substitute the coordinates of the given point (4, -3) into the equation to find the y-intercept, b. Using x = 4 and y = -3, we can solve for b:
-3 = -2(4) + b
-3 = -8 + b
b = -3 + 8
b = 5
Step 4: Now that we have the equation, y = -2x + 5, plot this line on the coordinate plane. We can start at the y-intercept (0, 5) and use the slope to find additional points to plot.
Step 5: To find another point on the line, we can use the slope. The slope, -2, tells us that for every 1 unit increase in the x-coordinate, the y-coordinate will decrease by 2 units. Starting from the y-intercept (0, 5), we can move 1 unit to the right, which brings us to the point (1, 3). Plot this point.
Step 6: Connect the two plotted points, (0, 5) and (1, 3), with a straight line. This line represents the equation y = -2x + 5.
Step 7: Extend the line in both directions, making sure it is straight and passes through the plotted points.