Question

Write in slope-intercept form the equation of the line passing through (1, -4) and (-3, 2).

A. y = -3/2x - \frac{5}{2}
B. y = 3/2}x - \frac{5}{2}
C. y = -3/2x + \frac{5}{2}
D. y = 3/2x + \frac{5}{2}

Answer 1

To write the equation of a line in slope-intercept form, find the slope using the given coordinates and then use the point-slope form of a line to write the equation. Simplify the equation to obtain the slope-intercept form.

So, the correct answer is: A. y = -3/2x - \frac{5}{2}

Step-by-step explanation:

To write the equation of a line in slope-intercept form, we need to find the slope and the y-intercept. The slope can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

Using the coordinates (1, -4) and (-3, 2), we can find the slope:

slope = (2 - (-4)) / (-3 - 1) = 6 / -4 = -3/2

Next, we can use the point-slope form of a line to write the equation:

y - y1 = m(x - x1)

Plugging in the values for (x1, y1) = (1, -4) and the slope m = -3/2, we get:

y - (-4) = -3/2(x - 1)

Simplifying the equation gives us:

y + 4 = -3/2x + 3/2

Finally, we can rewrite it in slope-intercept form y = mx + b by solving for y:

y = -3/2x + 3/2 - 4

y = -3/2x - 5/2