Use the point and the slope to graph each line. Write the equation of the line.
The line passes through point (–1, –4) and has slope –2.
recall the point-slope form, and you immediately get
y+4 = -2(x+1)
to graph the line, plot the point (-1,-4)
The next point is 1 to the right, and 2 down.
draw the line through the two points.
To graph the line, we can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
Where (x1, y1) represents the given point and m represents the slope.
The given point is (-1, -4) and the slope is -2. Substituting these values into the point-slope form equation, we get:
y - (-4) = -2(x - (-1))
Simplifying:
y + 4 = -2(x + 1)
Expanding the parentheses:
y + 4 = -2x - 2
To graph this line, we can start by setting up a coordinate plane and plotting the given point (-1, -4).
Next, we can find the y-intercept of the line by setting x = 0 in the equation:
y + 4 = -2(0) - 2
y + 4 = -2
This gives us a y-intercept of -2. So we can plot another point on the line at (0, -2).
Finally, we can draw a straight line passing through these two points.
To graph the line, we can use the point-slope form of the equation of a line: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Given that the point is (-1, -4) and the slope is -2, we can substitute these values into the point-slope form:
y - (-4) = -2(x - (-1))
y + 4 = -2(x + 1)
Next, we simplify the equation:
y + 4 = -2x - 2
To write the equation in slope-intercept form (y = mx + b), we need to isolate y:
y = -2x - 2 - 4
y = -2x - 6
Now, we have the equation of the line in slope-intercept form, y = -2x - 6.
To graph the line, we can plot the given point (-1, -4) on the coordinate plane and use the slope to identify the next point on the line.
Since the slope is -2, we can interpret it as "for every unit increase in x, y decreases by 2 units." Starting from the point (-1, -4), we can use this information to find another point.
For example, if we increase x by 1 unit, y would decrease by 2 units. So from (-1, -4), we can move one unit to the right and two units down to get the next point, which would be (-1 + 1, -4 - 2) = (0, -6).
Plotting the two points (-1, -4) and (0, -6) on the coordinate plane and connecting them with a straight line will give us the graph of the line that passes through the given point and has the given slope.