Question

1. Task Problem: Line j is represented by the following equation: y = 2x + 4. (1 points each)

a. What is the slope of line j? Show or explain how you got your answer.
b. What is the slope of any line that is parallel to line j? Explain your reasoning.
c. Write an equation for the line, k, that is parallel to line j and passes through the point with coordinates (3, 7). Show or explain how you got your answer.
d. Write an equation for the line, h, that is perpendicular to line j and passes through the point with coordinates (8, 10). Show or explain how you got your answer.

Answer 1

The equation y = 2x + 1 is the slope - intercept equation of the line.

The general form of the slope-intercept equation of the line is y = mx + b, where m is the slope and b is the y-intercept (i.e. the value of y-coordinate when the x-coordinate is zero).

Then you now know that the slope, m, of line j is 2 and the y-intercept is 4.

Answers:

a. slope = 3, as explainded above
b. Slope of any parallel to line J is the same slope of line J, i.e. 2.

The slope is a number that measures the inclination of the lines (rise/run) which is the same for parallel lines.

c. line k

m = 2 and point (3,7)

y - y1 = m(x - x1)

y - 7 = 2(x - 3)

y = 2x - 6 + 7
y = 2x + 1

d. line h

perpendicular => slope of line h = - 1 / slope of line j

slope of line h = - 1/2

point (8, 10) and y - y1 = -1/2 (x - x1) => y - 10 = -1/2 (x - 8)

y = -x/2 + 4 + 10 = -x/2 + 14