Question

What is an equation of the line that passes through the points left bracket, minus, 5, comma, minus, 8, right bracket(−5,−8) and left bracket, 5, comma, 4, right bracket(5,4)?

Answer 1

To find the equation of the line passing through two points, you can use the slope-intercept form, y = mx + b. By calculating the slope and using one of the points, you can find the equation of the line.

Step-by-step explanation:

To find the equation of the line that passes through two points, we can use the slope-intercept form: y = mx + b. First, let's find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1). Substituting the coordinates of the given points, we have: m = (4 - (-8)) / (5 - (-5)) = 12 / 10 = 1.2. Next, we need to find the y-intercept (b) by substituting one of the points and the slope into the equation. Let's use the point (5, 4): 4 = 1.2 * 5 + b. Solving for b, we get b = -1.

Therefore, the equation of the line is y = 1.2x - 1. This equation represents a line that passes through the points (-5, -8) and (5, 4).

Answer 2

The equation of the line that passes through the points (-5,-8) and (5,4) is calculated by finding the slope, which is 6/5, and then using the point-slope form to arrive at the final equation y = (6/5)x - 2.

Step-by-step explanation:

To find the equation of the line that passes through the points (-5,-8) and (5,4), we first need to determine the slope of the line. The slope, m, is calculated by the difference in y-coordinates divided by the difference in x-coordinates:

m = (y2 - y1) / (x2 - x1) = (4 - (-8)) / (5 - (-5)) = 12 / 10 = 6 / 5

With the slope known, we can use the point-slope form of a line, which is y - y1 = m(x - x1). Plugging in one of the points, for example (-5, -8), we get:

y - (-8) = (6/5)(x - (-5))

Simplifying the equation:

y + 8 = (6/5)x + 6

Finally, to get the equation in slope-intercept form (y = mx + b), we isolate y:

y = (6/5)x - 2

This is the equation of the line passing through the given points.