Find the gradient and the y-intercept of each of the following lines: (i) 5x – 10y = 3 (ii) (iii) x + 4 = 0 (iv) y = 6

Question

KnowledgeBoat · Accepted Answer

(i) Given, ⇒ 5x – 10y = 3 Converting 5x – 10y = 3 in the form y = mx + c we get, ⇒ -10y = 3 - 5x ⇒ y = ⇒ y = ⇒ y = The equation of straight line is given by, y = mx + c, where m is the slope and c is the y-intercept. Comparing, y = mx + c with y = , we get: m = slope = c = y-intercept = Hence, slope = . (ii) Converting in the form y = mx + c we get, The equation of straight line is given by, y = mx + c, where m is the slope and c is the y-intercept. Comparing y = mx + c with , we get: m = slope = c = y-intercept = 9 Hence, slope = , y-intercept = 9. (iii) Given, x + 4 = 0 x = -4 This is a vertical line parallel to the y-axis, passing through the x-axis at x = -4. We know that the inclination of a line parallel to y-axis is 90°. Slope of y-axis = tan 90° = infinity, which is not defined. Since the line is parallel to the y-axis and passes through a negative x-value, it never crosses the y-axis. There is no y-intercept. Hence, slope is not defined and line has no y-intercept. (iv) Given, y = 6 This is a horizontal line parallel to the x-axis, passing through the y-axis at y = 6. We know that the inclination of a line parallel to x-axis is 0°. Slope of a line parallel to x-axis = tan 0° = 0. y-intercept = 6 Hence, slope = 0 and y-intercept = 6.

Mathematics

Find the gradient and the y-intercept of each of the following lines: (i) 5x – 10y = 3 (ii) (iii) x + 4 = 0 (iv) y = 6

Straight Line Eq

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Find the gradient and the y-intercept of each of the following lines: (i) 5x – 10y = 3 (ii) (iii) x + 4 = 0 (iv) y = 6

Straight Line Eq

Related Questions

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Find the gradient and the equation of the line passing through the points:
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