Answer:
The Answer is: The slope is -1, so any line with the same slope is parallel.
Step-by-step explanation:
Given points (2, -7) and (4, -9) find the slope, m:
m = y - y1 / (x - x1)
m = -7 - (-9)/(2 - 4)
m = -7 + 9/-2
m = 2/-2
m = -1
A parallel line is any line with the same slope which is -1.
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The two lines are parallel when the slope of both the lines is the same. So, the line parallel to the line 'm' is the line whose slope is -1 and this can be determined by using the slope-intercept form.
Given :
Line m passes through the points (2, -7) and (4, -9).
To determine that line 'm' is parallel to which line, first, find the equation of line 'm' using a point-slope form of the line. The point-slope form is given by the equation:
[tex]\dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}[/tex] ----- (1)
where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the points on the line 'm'.
Now, put the values of [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in the equation (1).
[tex]\dfrac{y+7}{x-2}=\dfrac{-9+7}{4-2}[/tex]
[tex]\dfrac{y+7}{x-2}= -1[/tex]
y + 7 = -x + 2
y = -x - 5 ---- (2)
Now, using a slope-intercept form which is given by the equation:
y = mx + c ---- (3)
Now comparing equation (2) and (3) to find the slope and y-intercept.
m = -1
c = -5
The two lines are parallel when the slope of both the lines is the same. So, the line parallel to the line 'm' is the line whose slope is -1.
For more information, refer to the link given below:
https://brainly.com/question/19881501
