Question

Find an equation for a line satisfying the given conditions: through (-4, 3) and perpendicular to y = 2x - 3.

Answer 1

To find the equation of a line perpendicular to y = 2x - 3 and passing through the point (-4, 3), you can use the slope-intercept form of a line.

Step-by-step explanation:

The equation of the line perpendicular to y = 2x - 3 and passing through the point (-4, 3) can be found using the following steps:

1. First, determine the slope of the given line. The given line has a slope of 2.
2. Since the line we want is perpendicular, the slope of the line we want will be the negative reciprocal of the given slope. Therefore, the slope of the line we want is -1/2.
3. Using the slope-intercept form of a line, which is y = mx + b, we can substitute the slope (-1/2) and the coordinates of the point (-4, 3) into the equation to solve for the y-intercept, b.
4. Substituting the values, we have 3 = (-1/2)(-4) + b. Simplifying this equation, we get b = 2.
5. Finally, the equation of the line perpendicular to y = 2x - 3 and passing through (-4, 3) is y = (-1/2)x + 2.