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# AS Core concepts watch

1. How do you work out
"A line passes through the points (4,5) and (12, −9). Find the equation of the line in the form ay+ bx + c = 0"
Thank you
2. (Original post by laj61048)
How do you work out
"A line passes through the points (4,5) and (12, −9). Find the equation of the line in the form ay+ bx + c = 0"
Thank you
You can work out the gradient, using gradient, just the standard way. Now you can use the formula to get the equation of the line, and then just rearrange to give the answer in the form that is asked for.
3. Draw a sketch of the graph. Notice negative gradient (gradient = change in y/change in x). This allows calculation of y intercept and equation can be written in form y = ax + c rearrange this to obtain the form required.
gradient (-9-5)/(12-4) = -14/8 = -7/4 so reducing x by 4 will increase y by 7, y intercept (0,12), hence y = -7x/4 + 12 so y + 7x/4 - 12 = 0
so a = 1 , b = 7/4 and c = -12 equivalently -y - 7x/4 + 12 = 0 so a = -1 , b = -7/4 and c = 12

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