The equation of a line is given in point-slope form as
MATHEMATICS · Multi-part · A Level · Mathematics · Coordinate geometry in the (x y) plane · Coordinate geometry in the (x y) plane
Problem
The equation of a line is given in point-slope form as y+2=34(x−5). Answer the following.
(i) Rewrite the equation in slope-intercept form, clearly identifying the slope and the y-intercept.
(ii) Draw the graph of this line on suitable axes, indicating at least two accurately plotted points in addition to the intercept.
(iii) Write the equation of a second line that is parallel to the given line and passes through the origin, and draw its graph on the same axes.
(iv) Determine the coordinates of the points where each of the two lines meets the y-axis, and hence calculate the distance between these two points.