Find an equation for the line with the given properties
question: perpendicular to the line x − 2y = −5; containing the point (0, 4)

The first step here is to get the slope of the line by expressing the equation into the slope-intercept form, that is,

y = mx + b

where m is the slope and b is the y-intercept
therefore
y = 0.5x + 2.5

therefore the slope is 0.5. For the equation of the line perpendicular to the given line, the slope must be the negative intercept of the given line thus,

new slope (m2) = -(1/0.5) = -2

therefore the equation becomes

y = -2x + b

since it contains the point (0,4) therefore b = 4. The final equation is

y = -2x + 4 or 2x+y =4