Question

Write the slope-intercept form of the equation of the line through the given point and parallel to the given line.

a) (y = -1.25x + 0.65)
b) (y = 1.25x + 0.65)
c) (y = -1.25x - 0.65)
d) (y = 1.25x - 0.65)

B. Write the slope-intercept form of the equation of the line through the given point and perpendicular to the given line.
a) (y = 1.25x + 0.65)
b) (y = -1.25x - 0.65)
c) (y = 1.25x - 0.65)
d) (y = -1.25x + 0.65)

Answer 1

To write the slope-intercept form of an equation of a line parallel to a given line, use the same slope value. To write the slope-intercept form of an equation of a line perpendicular to a given line, use the negative reciprocal of the slope.

Step-by-step explanation:

To write the slope-intercept form of an equation of a line parallel to a given line, we need to use the same slope value as the given line. The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

For a line parallel to y = -1.25x + 0.65, the slope remains the same, which is -1.25. So the correct answer is (c) y = -1.25x - 0.65.

To write the slope-intercept form of an equation of a line perpendicular to a given line, we need to use the negative reciprocal of the slope of the given line. The negative reciprocal of 1.25 is -0.8.

For a line perpendicular to y = 1.25x + 0.65, the slope becomes -0.8. So the correct answer is (d) y = -0.8x + 0.65.