MATH SOLVE

4 months ago

Q:
# Consider the graph of the line y = x – 4 and the point (−4, 2). The slope of a line parallel to the given line is.A point on the line parallel to the given line, passing through (−4, 2), is .The slope of a line perpendicular to the given line is .A point on the line perpendicular to the given line, passing through (−4, 2), is .

Accepted Solution

A:

Answer: a. The slope of a line parallel to the given line is 1 b. A point on the line parallel to the given line, passing through (−4, 2), is (1,7) c. The slope of the line perpendicular to the given line is -1 d. A point on the line perpendicular to the given line, passing through (−4, 2), is (3,-5)Step-by-step explanation: The equation of the line in Slope-intercept form is: [tex]y=mx+b[/tex] Where m is the slope and b is the y-intercept. a. For the line [tex]y = x - 4[/tex] You can identify that: [tex]m=1[/tex] By definition, two lines are parallel if they have the same slope. Then, the slope of a line parallel to the given line is: [tex]m=1[/tex] b. The equation of the line in Point-slope form is: [tex]y -y_1 = m(x - x_1)[/tex] Where m is the slope and ([tex]x_1,y_1[/tex]) is a point of the line. Given the point (-4,2), substitute this point and the slope of the line into the equation: [tex]y -2 = (x +4)[/tex] Give a value to "x", substitute it into this equation and solve for "y": For [tex]x=1[/tex] : [tex]y -2 = (1 +4)[/tex] [tex]y= 5+2[/tex] [tex]y= 7[/tex] Then, you get the point (1,7) c. The slopes of perpendicular lines are negative reciprocals, then the slope of a line perpendicular to the given line is: [tex]m=-\frac{1}{1}\\\\m=-1[/tex] d. Given the point (-4,2), substitute this point and the slope of the line into the equation: [tex]y -2 = -1(x +4)[/tex] [tex]y -2 = -(x +4)[/tex] Give a value to "x", substitute it into this equation and solve for "y": For [tex]x=3[/tex] : [tex]y -2 = -(3 +4)[/tex] [tex]y= -7+2[/tex] [tex]y= -5[/tex] Then, you get the point (3,-5)