Which Equation Is The Equation Of A Line That Passes Through (-10 3) And Is Perpendicular To Y=5X-7

When first learning algebra, the equation of a line is one of the most important concepts to master. It helps students understand basic geometry and how to graph lines in different situations. But what happens when you are presented with an equation of a line that passes through two points and is perpendicular to another? This can be a tricky concept to wrap your head around, but it isn’t impossible. In this blog post we will explore which equation is the equation of a line that passes through (-10 3) and is perpendicular to y=5x-7.

The Slope-Intercept Form of a Line

The slope-intercept form of a line is y=mx+b, where m is the slope and b is the y-intercept. In order to find the equation of a line that passes through (-3,4) and is perpendicular to y=x-1, we can use the point-slope form of a line. The point-slope form of a line is y-y1=m(x-x1), where (x1,y1) is any point on the line and m is the slope. We know that the slope of a perpendicular line is the negative reciprocal of the slope of the original line, so in this case, the slope would be -1. We also know that the y-intercept must be 4, since that’s one of our given points. So our final equation would be y=-x+4.

The Point-Slope Form of a Line

In mathematics, the point-slope form of a line is an equation of a line that passes through a given point and has a given slope. The general form of the equation is y = mx + b, where m is the slope and b is the y-intercept. Given a point (x1, y1) and a slope m, the point-slope form of the equation of the line through (x1, y1) with slope m is:

y – y1 = m(x – x1)

This can be rewritten as:

y = mx – mx1 + y1

The advantage of using the point-slope form is that it is very easy to find the equation of a line when you know its slope and one point that it passes through.

The Standard Form of a Line

A line can be represented in various forms, but the most common form is the standard form of a line. The standard form of a line is represented by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. In order to find the equation of a line that passes through (-3,4) and is perpendicular to y=x-1, we need to find the slope of the given line and then use the point-slope form of a line. The point-slope form of a line is represented by the equation y – y1 = m(x – x1), where m is the slope of the line and (x1,y1) is any point on the line. In our case, we can choose (0,-1) as our point since it lies on both lines. Plugging in our values, we get: y – (-1) = -1(x – 0), which simplifies to y + 1 = -x. Therefore, the equation of our desired line is y = -x + 1.

How to Find the Equation of a Line That Passes Through Two Points

To find the equation of a line that passes through two points, we need to find the slope of the line and then use that slope to write the equation. To find the slope, we need to use the formula:

Slope = (y2-y1)/(x2-x1)

In this formula, “y2” and “y1” are the y-coordinates of the two points, and “x2” and “x1” are the x-coordinates of the two points. Once we have the slope, we can use it to write the equation of the line in slope-intercept form:

y = mx + b

In this equation, “m” is the slope and “b” is the y-intercept. To find “b”, we just need to plug one of our points into the equation and solve for “b”.

How to Find the Equation of a Perpendicular Line

Assuming you already know how to find the equation of a line in slope-intercept form, finding the equation of a perpendicular line is simply a matter of finding the negative reciprocal of the original line’s slope and solving for y. For example, if we have the line y=2x+5 and we want to find a perpendicular line that passes through the point (-1, 3), we would first take the negative reciprocal of 2 (which is -1/2) and plug it into our equation as follows: y=-1/2x+b. We can then solve for b by plugging in our known point (-1, 3) and solving for b:

3=-1/2(-1)+b
3=1/2+b
3.5=b

Therefore, our final equation is y=-1/2x+3.5

Conclusion

As we can see, the equation for a line that passes through (-10 3) and is perpendicular to y=5x-7 is y=-1/5 x + 13. The process of finding this equation is straightforward as long as you have a basic understanding of how linear equations work. Knowing how to solve problems like these will give you an advantage when it comes to solving math problems in the future.