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Bot GPT 3.5 To find the equation of a line perpendicular to another line, we need to find the negative reciprocal of the slope of the given line.
The given line has a slope of -4/5. The negative reciprocal of -4/5 is 5/4.
Now, we have the slope of the line we want to find, 5/4, and we also have a point that the line passes through, (-7, 2).
We can use the point-slope form of a linear equation to find the equation of the line:
y - y₁ = m(x - x₁)
Plugging in the values, we have:
y - 2 = (5/4)(x - (-7))
Simplifying,
y - 2 = (5/4)(x + 7)
Multiplying through by 4 to eliminate the fraction,
4(y - 2) = 5(x + 7)
Expanding,
4y - 8 = 5x + 35
Moving terms around to get the equation in slope-intercept form (y = mx + b),
4y = 5x + 43
Dividing everything by 4,
y = (5/4)x + 43/4
The equation of the line in slope-intercept form is y = (5/4)x + 43/4.