Question

The graph of a linear equation passes through the points (-4,1) and (4,6)

HELP!

Answer 1

a) (0, 3.5)

b) (12, 11)

Explanation:

The points through which the graph of the linear equation passes are;

(-4, 1) and (4, 6)

The slope of the equation of a straight line passing through points (x₁, y₁), and (x₂, y₂), 'm', is given as follows;

`Slope, \, m =(y_(2)-y_(1))/(x_(2)-x_(1))`

∴ The slope of the equation, m = (6 - 1)/(4 - (-4)) = 5/8 = 0.625

The equation of th line in point and slope form is therefore;

y - 1 = 0.625·(x - (-4))

∴ y = 0.625·(x - (-4)) + 1 = 0.625·x + 3.5

y = 0.625·x + 3.5

Therefore;

a) When x = 0, y = 0.625 × 0 + 3.5 = 3.5

∴ The point (0, 3.5) is a solution

b) When x = 12, we have, y = 0.625 × 12 + 3.5 = 11

∴ The point (12, 11) is a solution

However;

c) When x = 8, we have, y = 0.625 × 8 + 3.5 = 8.5

∴ The point (8, 5) is not a solution

d) When x = -6, we have, y = 0.625 × (-6) + 3.5 = -0.25

∴ The point (-6, 0) is not a solution

Therefore;

The points which are solutions are;

(0, 3.5) and (12, 11)