Write the equation in slope-intercept form through the point (-5, 3) and is perpendicular to the line y = 2x - 3 and graph
1 answer:
Slope intercept form: y = mx + b
When a line is perpendicular to another line, its slope is the negative reciprocal to that slope.
From this information, we already know that the slope of our new line is -1/2, because -1/2 is the negative reciprocal to 2 (which is the slope of the original line).
y = -1/2x + b
Because the point (-5,3) is given, we can simply plug the x and y coordinates into our incomplete equation.
3 = -1/2(-5) + b
3=2.5 + b
b = 0.5
ANSWER: y = -1/2x + 0.5
THE GRAPH IS LINKED; RED LINE IS y=2x-3 AND BLUE LINE IS y=-1/2x + 0.5
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- The coordinates of a point satisfies the equation of a line if the point lies on the line
- If a single point satisfies the equations of two lines, the point is on both lines, so the lines will intersect at that point.
- This means that each point where the two lines touch is a solution to the system of equations
- This means that if you substitute the x and y values of the point for x and y in the equations, both equations will be true
You haven't given any option. However, I have tried to complete this question according to what we know about system of linear equations. Suppose you have the following system of two linear equations in two variables:
The fist equation is the blue one and the second equation is the red one. Both have been plotted in the first figure below. As you can see, (-3, -3) is the point of intersection and lies on both lines. So this point is a solution of the system of equation and we can also say that it touches both lines. On the other hand, if you substitute the x and y values of the point for x and y in the equations, both equations will be true, that is:
Also, you can have a system with infinitely many solutions as the following:
Here, every point that is solution of the first equation is solution of the second one. That is because both equations are basically the same. If we divide eq (2) by 2, then we get eq (1).
<h2>Learn more:</h2>System of linear equations in real life problems: brainly.com/question/10412788
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