How do you write an equation of a line passing through (0,2) and (-5,0)?

Question

Eva Adamson · Accepted Answer

See a solution process below:

First, we need to determine the slope of the line going through these two points. The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))# Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line. Substituting the values from the points in the problem gives: #m = (color(red)(0) - color(blue)(2))/(color(red)(-5) - color(blue)(0)) = (-2)/-5 = 2/5# We can now use the slope-intercept formula to write the equation for the line. The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)# Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value. We calculated the slope above. The y-intercept is #(0, 2)#. Substituting into the formula gives: #y = color(red)(2/5)x + color(blue)(2)#

Eva Adamson · Answer

undefined To write the equation of a line passing through the points $(0,2)$ and $(-5,0)$, use the point-slope form:

$ y - y_1 = m(x - x_1) $

where $ (x_1, y_1) $ is a point on the line, and $ m $ is the slope of the line.

1. Calculate the slope using the given points: 
   $ m = \frac{y_2 - y_1}{x_2 - x_1} $
   $ m = \frac{0 - 2}{-5 - 0} = \frac{-2}{-5} = \frac{2}{5} $

2. Choose one of the given points, say $(0,2)$, and substitute the values into the point-slope form:
   $ y - 2 = \frac{2}{5}(x - 0) $

3. Simplify the equation:
   $ y - 2 = \frac{2}{5}x $

4. To get the equation in slope-intercept form (y = mx + b), solve for y:
   $ y = \frac{2}{5}x + 2 $

The equation of the line passing through $(0,2)$ and $(-5,0)$ is $ y = \frac{2}{5}x + 2 $.