Question

What is the equation of the line that passes through the point (5, 4) and is perpendicular to the line whose equation is 2x + y = 3 in standard form?

Answer 1

The equation of the line passing through the point (5, 4) and perpendicular to the line with equation 2x + y = 3 is y = ½x + 1.5.

Step-by-step explanation:

To find the equation of a line that is perpendicular to another line, we first need to understand the concept of slope. The slope of a line is the representation of its steepness and is typically written as 'm' in the equation y = mx + b, where 'b' is the y-intercept. The given line has an equation 2x + y = 3, which can be rewritten in slope-intercept form (y = mx + b) by subtracting 2x from both sides, yielding y = -2x + 3. The slope of this line is -2.

Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of the line we want to find is the negative reciprocal of -2, which is ½. Now that we have the slope, we can use the point (5, 4) and the slope to find the y-intercept 'b' using the formula y = mx + b by plugging in the values: 4 = (½)(5) + b, solving b = 4 - (½)(5) = 1.5.

The equation of the line passing through (5, 4) and perpendicular to 2x + y = 3 is therefore y = ½x + 1.5.

Answer 2

So a line that is perpendicular is a line that intercepts other line at a 90 degree angle.

Slope of perpendicular lines is the opposite sign and the reciprocal of the other.

So if your slope was 2 the perpendicular line would have a slope of -1/2.

So the equation, 2x + y = 3

Can be rewritten as

y= -2x+3

Perpendicular slope: 1/2

Since it intercepts/ passes the coordinates (5,4) it means that those values are included in the function input x and output y.

y=mx+b

4=1/2(5)+b

Solve for b (y intercept)

4-2.5=b

1.5=b

So the equation of the perpendicular is

y=1/2x+3/2 or y=.5x+1.5