Question

Find the equation of the line passing through points (-5,4) and (-3,2)

Answer 1

The equation of the line passing through points (-5, 4) and (-3, 2) is found using the slope formula and the point-slope form, which results in the final equation y = -x + 3.

Step-by-step explanation:

To find the equation of the line passing through two points, first, we need to find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the given points (-5, 4) and (-3, 2) into the formula gives us:
m = (2 - 4) / (-3 + 5) = (-2) / 2 = -1.

Next, we use the point-slope form of a line which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Substituting the slope and one of the points, for example (-5, 4), we get:
y - 4 = -1(x + 5).

Simplifying the equation by distributing the slope on the right side and then adding 4 to both sides, we get the equation of the line in slope-intercept form:
y = -1x - 1 + 4
y = -x + 3.

The equation of the line passing through points (-5, 4) and (-3, 2) is y = -x + 3.

Answer 2

The equation of the line passing through the points (-5,4) and (-3,2) is y = -x - 1, found by determining the slope and then using point-slope form.

Step-by-step explanation:

The question asks us to find the equation of a line passing through the points (-5,4) and (-3,2). To find the equation of a line, we first need to determine the slope (m) using the formula:

m = (y_2 - y_1) / (x_2 - x_1)

Plugging in the coordinates of the given points gives us:

m = (2 - 4) / (-3 + 5) = (-2) / (2) = -1

Now that we have the slope, we can use the point-slope form to write the equation of the line: y - y_1 = m(x - x_1). Using one of the given points (-5,4), the equation becomes:

y - 4 = -1(x + 5)

Expanding and simplifying:

y - 4 = -x - 5

y = -x - 1

This is the equation of the line in slope-intercept form, showing that the slope is -1 and the y-intercept is -1.