Question

Please help me! Ignore the answer I put, I know it’s wrong

Answer 1

y = - x - 2

Explanation:

Perpendicular definition is two slopes multiply each others and equal to -1, can be expressed in equation as:

`\displaystyle{m_1m_2 = - 1}`

m represents the slope value. To find another slope that is perpendicular to each other, we find another m-value. We know our first slope is given in the question which is 1 (y = x has slope of 1). Therefore:

`\displaystyle{1m_2 = - 1} \\ \\ \displaystyle{m_2 = - 1}`

Therefore, another slope that is perpendicular to 1 is -1. We know the slope perpendicular, we substitute in the equation y = mx + b:

`\displaystyle{y = - 1x + b} \\ \\ \displaystyle{y = - x + b}`

Next, we find the y-intercept (b). We are given the point that the perpendicular line passes through, (-4,2). Substitute x = -4 and y = 2 in the equation above:

`\displaystyle{ 2 = - ( - 4) + b} \\ \\ \displaystyle{2 = 4 + b} \\ \\ \displaystyle{2 -4 = b} \\ \\ \displaystyle{ - 2 = b}`

Therefore, b = -2, substitute in:

`\displaystyle{y = - x - 2}`

Therefore, the equation that is perpendicular to y = x and also passes through (-4,2) is y = - x - 2