Write an equation in slope-intercept form of the line that passes through (-4,5) and (2,-6) .
A) $y = \frac { 11 } { 6 } x - \frac { 7 } { 3 }$
B) $y = - \frac { 7 } { 3 } x + \frac { 11 } { 6 }$
C) $y = - \frac { 7 } { 3 } x - \frac { 11 } { 6 }$
D) $y = - \frac { 11 } { 6 } x - \frac { 7 } { 3 }$
E) $y = \frac { 11 } { 6 } x + \frac { 7 } { 3 }$

Question

Quizplus · Accepted Answer

We can use the formula for slope, which is:

slope = (change in y) / (change in x)

Using the points (-4, 5) and (2, -6), we have:

slope = (-6 - 5) / (2 - (-4))
slope = (-11) / 6

Now that we have the slope, we can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

Using the point (-4, 5), we have:

y - 5 = (-11/6)(x - (-4))

Simplifying:

y - 5 = (-11/6)(x + 4)
y = (-11/6)x - (44/6) + 5
y = (-11/6)x - (29/6)

This is in slope-intercept form, where the slope is -11/6 and the y-intercept is (0, -29/6). Option D matches this equation, so it is the correct choice.

Write an Equation in Slope-Intercept Form of the Line That y=116x−73y = \frac { 11 } { 6 } x - \frac { 7 } { 3 }y=611​x−37​

Write an Equation in Slope-Intercept Form of the Line That $y = \frac { 11 } { 6 } x - \frac { 7 } { 3 }$