Question

Write the equation of a line in slope-intercept form that passes through (4,4) and (-2,-5).

a) y = -3x + 16

b) y = 3x - 8

c) y = -3x - 8

d) y = 3x + 16

Answer 1

The correct equation of the line in slope-intercept form is option (c) y = -3x - 8.

Step-by-step explanation:

To find the equation of the line in slope-intercept form (y = mx + b), we can use the given points (4,4) and (-2,-5). First, calculate the slope (m) using the formula (m = (y2 - y1) / (x2 - x1)). Plugging in the coordinates, we get:

`\[ m = (-5 - 4) / (-2 - 4) = -9 / -6 = 3/2. \]`

Now that we have the slope, we can use one of the points and the slope in the equation y = mx + b to find the y-intercept (b). Let's use the point (4,4):

`\[ 4 = (3/2)(4) + b. \]`

Solving for b, we get:

`\[ b = 4 - 6 = -2. \]`

Now, we can write the equation of the line:

`\[ y = (3/2)x - 2. \]`

To convert it into the slope-intercept form, multiply both sides by 2 to get rid of the fraction:

`\[ 2y = 3x - 4. \]`

Finally, add 4 to both sides to isolate y:

`\[ 2y = 3x - 4 + 4 \]`

`\[ 2y = 3x. \]`

Divide both sides by 2:

`\[ y = (3/2)x. \]`

Comparing this with the given options, we see that option (c) y = -3x - 8.