Question

Write an equation of the line through the given point (2, 2) with the given slope m = -4. Write the equation in slope-intercept form. Enter your answer with NO SPACES.

Answer 1

y=-4x+10

Explanation:

We can apply point-slope form since we are given with point and slope:

`\displaystyle{y - y_1 = m(x - x_1)}`

Move y1 to the other side, this is point-slope form in slope-intercept variant:

`\displaystyle{y = m(x - x_1) + y_1}`

We know that the point is (2,2) and slope is m = -4. Subtitute in known values:

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

The slope-intercept form is in y = mx + b where m is slope and b is y-intercept. Therefore, expand the term in:

`\displaystyle{y = - 4x + 8+2} \\ \\ \displaystyle{y = - 4x +10}`

Therefore, the equation is y = -4x + 10