Find an equation for the line that passes through the points (−5, -2) and (5, 3)

Question

Find an equation for the line that passes through the points (−5, -2)

 and( 5, 3)

Answer 1

First, we find the slope of the line:

slope = (change in y) / (change in x) = (3 - (-2)) / (5 - (-5)) = 5/10 = 1/2

Next, we use one of the points, say (-5,-2), and the slope to write the equation of the line in point-slope form:

y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point

y - (-2) = (1/2)(x - (-5))

y + 2 = (1/2)(x + 5)

Finally, we can simplify this equation into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept:

y + 2 = (1/2)x + (5/2)

y = (1/2)x + (1/2)

Therefore, the equation of the line passing through the points (-5,-2) and (5,3) is y = (1/2)x + (1/2).