Find the equation of the line that passes through the point (−2,−3)(−2,−3), with gradient 2552 . Give your answer in the form: 𝑎𝑥+𝑏𝑦+𝑐ax+by+c==00
Question
Find the equation of the line that passes through the point (−2,−3), with gradient 2552.
Give your answer in the form:
Solution
The equation of a line in slope-intercept form is given by y = mx + c, where m is the slope (or gradient) and c is the y-intercept.
Given that the line passes through the point (-2,-3) and has a gradient of 5/2, we can substitute these values into the equation to find the y-intercept.
-3 = (5/2)(-2) + c -3 = -5 + c c = -3 + 5 c = 2
So, the equation of the line in slope-intercept form is y = (5/2)x + 2.
To convert this to the form ax + by + c = 0, we can multiply through by 2 to get rid of the fraction:
2y = 5x + 4 -5x + 2y - 4 = 0
So, the equation of the line in the form ax + by + c = 0 is -5x + 2y - 4 = 0.
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