inequality in slope intercept form calculator

Inequality in Slope Intercept Form Calculator: A Comprehensive Guide

When it comes to solving linear equations, one of the most important concepts is the slope-intercept form calculator. This tool allows us to find the equation of a line given its slope (m) and y-intercept (b). However, what if we want to find the intersecting point of two perpendicular lines that do not intersect on the y-axis? Can we still use the slope-intercept form calculator to achieve this?

The answer is yes. To begin with, let's review how to use the slope-intercept form calculator. Given a line with a slope (m) and y-intercept (b), we can write its equation as:

y = mx + b

For example, if we know that the slope of a line is 1/2 and its y-intercept is 5, we can write its equation as:

y = 1/2x + 5

Now, let's say we have two perpendicular lines with slopes m1 and m2, respectively. If we want to find their intersecting point without using a graph, we can start by finding the slope of one of the lines. For instance, if we know that the line (2,6) is perpendicular to y = -2x, then we can find its slope by solving for m:

m = 1/2

Next, we need to find the equation of this line in slope-intercept form. To do this, we can use the point-slope form formula:

y - y1 = m(x - x1)

Substituting the values we know, we get:

y - 6 = (1/2)(x - 2)

Simplifying this equation, we get:

y = 1/2x + 5

Now that we have the equation of one line, we can use it to find the intersecting point of the two lines. To do this, we need to solve for the y-coordinate of the intersecting point. This involves substituting the values of x and m into the equation of the line.

For example, if we want to find the intersecting point of the line (2,6) and (-2,4), we can substitute these values into the equation:

y = 1/2x + 5

Simplifying this equation, we get:

y = 1/2(-2) + 5

y = -1 + 5

y = 4

Therefore, the intersecting point of the two lines is (-2,4).

In conclusion, using the slope-intercept form calculator, we can find the intersecting point of two perpendicular lines that do not intersect on the y-axis without relying on a graph. This involves finding the equation of one line, substituting values into this equation to solve for the y-coordinate of the intersecting point, and then using this value to find the x-coordinate.

Inequality in slope intercept form calculator