Question

Write an equation in slope-intercept form for the line passing through the pair of points.

(–1, 2), (4, –3)

a. y = 0x + 1

b. y = –x – 1

c. y = 0x – 1

d. y = –x + 1

Answer 1

Find the slope m.

m = (-3 -2)/(4 - (-1))

m = -5/(4 + 1)

m = -5/5

m = -1

Plug the slope and one of the points into the point-slope formula.

y - y_1 = m(x - x_1)

y - 2 = -1(x -(-1))

y - 2 = -1(x + 1)

The goal is to isolate y.

y - 2 = -x - 1

y = -x - 1 + 2

y = -x + 1

The answer is choice d.

Do you understand what I did here?

Answer 2

`\boxed{d. \quad y = -x  + 1}}`

Explanation:

The equation for a straight line is

y = mx + b

where m is the slope of the line and b is the y-intercept.

The line passes through the points (-1, 2) and (4, -3)

(a) Calculate the slope of the line

`\begin{array}{rcl}m & = & (y_(2) - y_(1))/(x_(2) - x_(1))\\\\ & = & (-3 - 2 )/(4 - (-1))\\\\& = & (-5)/(5)\\\\& = & -1\\\end{array}`

(b) Find the y-intercept

Insert the coordinates of one of the points into the equation

`\begin{array}{rcl}y & = & mx + b\\-3 & = & (-1)4 + b \\-3 & = & -4 + b\\b & = & 1\\\end{array}`

(c) Write the equation

The y-intercept is at x = 1.

`\text{The equation for the line is $\boxed{\mathbf{y = -x  + 1}}$}`

The diagram shows the graph of the line passing through the two points with slope = -1.