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A line l2 is perpendicular to the line x + 2y – 5 = 0 without computing the gradient of this
line find the equation of l2 if it passes through (3, 4)​

Sagot :

Amysun2025idn

Answer:

y=2x-2

Step-by-step explanation:

first, let's put the line into y=mx+b form (slope-intercept form), where m is the slope (or gradient) and b is the y intercept

add 5 to both sides

x+2y=5

subtract x from both sides

2y=-x+5

divide by 2

y=-1/2x+5/2

perpendicular lines have slopes (gradients) that are negative (one is positive, another one is negative) and reciprocal (they are essentially the same number, just "flipped")

to find the slope of I2:

since -1/2 is negative, that means the slope of I2 will be 2 (2/1 is the reciprocal of 1/2 (positive version of -1/2))

so here's our equation so far:

y=2x+b

now we need to find b

because line will pass through (3,4), we can use it to solve for b

substitute 4 as y and 3 as x

4=2(3)+b

multiply

4=6+b

-2=b

therefore the equation is y=2x-2

hope this helps!!

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