A straight line with the equation y=ax-3 goes through the point (2,11). Work out the value of a
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The linear equation is y = -x - 6
Step-by-step explanation:
To form a linear equation from two points lie on the line which the equation represented it
- Find the slope of the line by using the formula
- Then use the slope-intercept form of the equation y = m x + b
- To find the value of b substitute x and y of the equation by the coordinates of one of the two given points
∵ Points (-2 , -4) and (-3 , -3) lie on the line
∴ = -2 and
= -3
∴ = -4 and
= -3
- Substitute these values in the formula of the slope
∵
∴ m = -1
∵ The form of the equation is y = m x + b
∵ m = -1
∴ y = (-1) x + b
∴ y = -x + b
To find b substitute x and y in the equation by the coordinates of
point (-2 , -4) OR (-3 , -3)
∵ x = -3 and y = -3
∴ -3 = -(-3) + b
∴ -3 = 3 + b
- Subtract 3 from both sides
∴ -6 = b
∴ The equation is y = -x + (-6)
∴ y = -x - 6
The linear equation is y = -x - 6
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