Consider the line

MATHEMATICS · Multi-part · CBSE · Mathematics · Straight Lines · Straight Lines

Problem

Consider the line 7x+4y−28=07x + 4y - 28 = 0. Answer the following: (a) Part 1: (i) Rewrite the equation in the form y=mx+cy = mx + c and hence state the slope and the yy-intercept. (b) Part 2: (ii) Find the xx-intercept of the line. (c) Part 3: (iii) Sketch the line on a Cartesian plane, clearly indicating both intercepts. (d) Part 4: (iv) The line together with the coordinate axes encloses a triangle in the first quadrant. Calculate the area of this triangle. (e) Part 5: (v) A point P(t,0)P(t, 0) is chosen on the xx-axis such that the area of △OPQ\triangle OPQ is 42 square units, where OO is the origin and QQ is the yy-intercept. Find the two possible values of tt.

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