Answer:
a) (0, 3.5)
b) (12, 11)
Step-by-step 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;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
∴ 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)
