Find the equation of the line containing the point whose coordinates are (1, 2)and parallel to the graph of 5x + y = −4.
the line has slope -5, so now you have a point and a slope:
y-2 = -5(x-1)
To find the equation of a line that is parallel to the given line, we need to find the slope of the given line. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope of the line.
Rearranging the given equation 5x + y = -4 into the slope-intercept form, we get:
y = -5x - 4
From this equation, we can identify that the slope of the given line is -5.
Since the line we're looking for is parallel to the given line, it will have the same slope, which is -5. As a result, the equation of the line parallel to the given line will also have a slope of -5.
Now, let's use the point-slope form of a linear equation to find the equation of the line.
The point-slope form is given by: y - y1 = m(x - x1)
Where (x1, y1) represents the coordinates of the given point, and m represents the slope of the line.
Plugging in the values, we have the point (1, 2) and a slope of -5:
y - 2 = -5(x - 1)
Simplifying further, we get:
y - 2 = -5x + 5
Finally, rearranging the equation to the slope-intercept form, we have:
y = -5x + 7
Therefore, the equation of the line containing the point (1, 2) and parallel to the graph of 5x + y = -4 is y = -5x + 7.